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alg-geom/9210001
|
Arrangements of Hyperplanes and Vector Bundles on $P^n$
|
Any arrangement of hyperplanes in general position in $P^n$ can be regarded
as a divisor with normal crossing. We study the bundles of logarithmic 1-forms
corresponding to such divisors` from the point of view of classification of
vector bundles on $P^n$. It turns out that all such bundles are stable. The
study of jumping lines of these bundles gives a unified treatment of several
classical constructions associating a curve to a collection of points in $P^n$.
The main result of the paper is "Torelli theorem" which says that the
collection of hyperplanes can be recovered from the isomorphism class of the
corresponding logarithmic bundle unless the hyperplanes ocsulate a rational
normal curve. In this latter case our construction reduces to that of secant
bundles of Schwarzenberger.
| 1992-10-06
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
I.Dolgachev and M.Kapranov
|
alg-geom/9209001
|
On the $(-1)$-curve conjecture of Friedman and Morgan
|
Main difference with previous version: we prove that every differentiably
embedded sphere with self intersection $-1$ in a simply connected algebraic
surface with $p_g >0$ is homologous to a $(-1)$-curve if $|K_{\min}|$ contains
a smooth irreducible curve of genus at least 2 and $p_g$ is even or $K_{\min}^2
\not\equiv 7 \pmod8$ (here $K_{\min}$ is the canonical class of the minimal
model).
| 1992-09-12
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Rogier Brussee
|
alg-geom/9208004
|
Torsion Sections of Semistable Elliptic Surfaces
|
Let S be a torsion section of an elliptic surface with only I_n fibers. This
article addresses the question: which components of singular fibers can S pass
through? We give necessary criteria for the "component numbers", and show an
equidistribution result for torsion sections of prime order.
| 1992-08-21
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Rick Miranda
|
alg-geom/9208003
|
Weierstrass weight of Gorenstein singularities with one or two branches
|
Let $X$ denote an integral, projective Gorenstein curve over an algebraically
closed field $k$. In the case when $k$ is of characteristic zero, C. Widland
and the second author have defined Weierstrass points of a line bundle on $X$.
In the first section, this definition is extended to linear systems in
arbitrary characteristic. This definition may be viewed as a generalization of
the definitions of Laksov and St\"ohr-Voloch to the Gorenstein case. In the
second section, an example is given to illustrate the definition. This example
is a plane curve of arithmetic genus 3 in characteristic 2 such that the gap
sequence at every smooth point (with respect to the dualizing bundle) is 1,2,5
and there are no smooth Weierstrass points. In the third section, the
Weierstrass weight of a unibranch singularity (on a not necessarily rational
curve) is computed in terms of its semigroup of values. In the final section,
the Weierstrass weight of a singularity with precisely two branches (again
assuming that the characteristic is zero) is computed.
AMS Classification: Primary 14H55, Secondary 14H20.
| 1992-08-20
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
A. Garcia and R.F. Lax
|
alg-geom/9208002
|
Abelian varieties over Q and modular forms
|
This paper gives a conjectural characterization of those elliptic curves over
the field of complex numbers which "should" be covered by standard modular
curves. The elliptic curves in question all have algebraic j-invariant, so they
can be viewed as curves over Q-bar, the field of algebraic numbers. The
condition that they satisfy is that they must be isogenous to all their Galois
conjugates. Borrowing a term from B.H. Gross, "Arithmetic on elliptic curves
with complex multiplication," we say that the elliptic curves in question are
"Q-curves." Since all complex multiplication elliptic curves are Q-curves (with
this definition), and since they are all uniformized by modular forms
(Shimura), we consider only non-CM curves for the remainder of this abstract.
We prove:
1. Let C be an elliptic curve over Q-bar. Then C is a Q-curve if and only if
C is a Q-bar simple factor of an abelian variety A over Q whose algebra of
Q-endomorphisms is a number field of degree dim(A). (We say that abelian
varieties A/Q with this property are of "GL(2) type.")
2. Suppose that Serre's conjecture on mod p modular forms are correct (Ref:
Duke Journal, 1987). Then an abelian variety A over Q is of GL(2)-type if and
only if it is a simple factor (over Q) of the Jacobian J_1(N) for some integer
N\ge1. (The abelian variety J_1(N) is the Jacobian of the standard modular
| 1992-08-06
| 2015-06-30
|
[
"alg-geom",
"math.AG"
] |
Kenneth A. Ribet
|
alg-geom/9208001
|
Open String Diagrams I: Topological Type
|
An arbitrary Feynman graph for string field theory interactions is analysed
and the homeomorphism type of the corresponding world sheet surface is
completely determined even in the non-orientable cases. Algorithms are found to
mechanically compute the topological characteristics of the resulting surface
from the structure of the signed oriented graph. Whitney's
permutation-theoretic coding of graphs is utilized.
| 1992-08-03
| 2009-10-22
|
[
"alg-geom",
"hep-th",
"math.AG"
] |
Subhashis Nag and Parameswaran Sankaran (The Institute of Mathematical
Sciences C.I.T.Campus Madras)
|
alg-geom/9207001
|
Completions of mapping class groups and the cycle $C - C^-$
|
In this paper we study the proalgebraic completion of mapping class relative
to their maps to the symplectic group. The main result is that the natural map
from the unipotent (a.k.a. Malcev) completion of the Torelli group to the
prounipotent radical of the Sp_g completion of the mapping class group is a non
trivial central extension with kernel isomorphic to Q, at least when g \ge 8.
The theorem is proved by relating the central extension to the line bundle
associated to the archemidean height of the cycle C - C- in the Jacobian of the
curve C. We also develop some of the basic theory of relative completions.
| 1992-07-23
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Richard Hain (Duke Univeristy)
|
alg-geom/9206009
|
The complex separation and extensions of Rokhlin congruence for curves
on surfaces
|
The subject of this paper is the problem of arrangement of real algebraic
curves on real algebraic surfaces. In this paper we extend Rokhlin,
Kharlamov-Gudkov-Krakhnov and Kharlamov-Marin congruences for curves on
surfaces and give some applications of this extension.
For some pairs consisting of a surface and a curve on this surface (in
particular for M-pairs) we introduce a new structure --- the complex separation
that is separation of the complement of curve into two surfaces. In accordance
with Rokhlin terminology the complex separation is a complex topological
characteristic of real algebraic varieties. The complex separation is similar
to complex orientations introduced by O.Ya.Viro (to the absolute complex
orientation in the case when a curve is empty and to the relative complex
orientation otherwise). In some cases we calculate the complex separation of a
surface (for example in the case when surface is the double branched covering
of another surface along a curve). With the help of these calculations
applications of the extension of Rokhlin congruence gives some new restrictions
for complex orientations of curves on a hyperboloid.
| 1992-06-24
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
G.Mikhalkin
|
alg-geom/9206008
|
The fibers of the Prym map
|
In this work we use the bigonal, trigonal and tetragonal constructions to
describe the fibers of the Prym map P : R_{g} ---->A_{g-1} inthe cases when it
is dominant, i.e. for g < 7. The most interesting cases are g = 5, where the
fiber is a double cover of the Fano surface of lines on a cubic threefold, and
g=6, where the map is generically finite (of degree 27) with Galois group
WE_{6}, so that the general fiber has the structure of the 27 lines on a cubic
surface. For g > 6, the map is known to be generically injective. The
tetragonal construction gives many counterexamples to injectivity, and we
conjecture that all noninjectivity is due to the tetragonal construction.
| 1992-06-17
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Ron Donagi
|
alg-geom/9206007
|
Rang de courbes elliptiques d'invariant donne
|
We prove that there exist infinitely many elliptic curves over \Q with given
modular invariant, and rank >=2. Furthermore, there exist infinitely many
elliptic curves over $\Q$ with invariant equal at 0 (resp. 1728) and rank >=6
(resp. >=4).
| 1992-06-16
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Jean-Francois Mestre
|
alg-geom/9206006
|
Corps quadratiques dont le 5-rang du groupe des classes est >=3
|
We prove the existence of infinitely many real and imaginary fields whose
5-rank of the class group is >=3.
| 1992-06-16
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Jean-Francois Mestre
|
alg-geom/9206005
|
Two Two-dimensional Terminations
|
Varieties with log terminal and log canonical singularities are considered in
the Minimal Model Program, see \cite{...} for introduction. In
\cite{shokurov:hyp} it was conjectured that many of the interesting sets,
associated with these varieties have something in common: they satisfy the
ascending chain condition, which means that every increasing chain of elements
terminates. Philosophically, this is the reason why two main hypotheses in the
Minimal Model Program: existence and termination of flips should be true and
are possible to prove.
In this paper we prove that the following two sets satisfy the ascending
chain condition:
1. The set of minimal log discrepancies for $K_X+B$ where $X$ is a surface
with log canonical singularities.
2. The set of groups $(b_1,...b_s)$ such that there is a surface $X$ with log
canonical and numerically trivial $K_X+\sum b_jB_j$. The order on such groups
is defined in a natural way.
| 1992-06-12
| 2015-06-30
|
[
"alg-geom",
"math.AG"
] |
Valery Alexeev
|
alg-geom/9206004
|
Extremal Rays and Null Geodesics on a Complex Conformal Manifold
|
This is a revised version of the paper submitted before.
| 1992-06-11
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Yun-Gang Ye
|
alg-geom/9206003
|
Affine like Surfaces
|
We classify smooth surfaces whose higher cohomologies of i-forms for all i
vanish. We show that if such a surface is not affine, then it has essentially
two possibilities.
| 1992-06-04
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
N. Mohan Kumar
|
alg-geom/9206002
|
String Branchings on Complex Tori and Algebraic Representations of
Generalized Krichever-Novikov Algebras
|
The propagation differential for bosonic strings on a complex torus with
three symmetric punctures is investigated. We study deformation aspects between
two point and three point differentials as well as the behaviour of the
corresponding Krichever-Novikov algebras. The structure constants are
calculated and from this we derive a central extension of the Krichever-Novikov
algebras by means of b-c systems. The defining cocycle for this central
extension deforms to the well known Virasoro cocycle for certain kinds of
degenerations of the torus.
AMS subject classification (1991): 17B66, 17B90, 14H52, 30F30, 81T40
| 1992-06-03
| 2009-10-22
|
[
"alg-geom",
"math.AG"
] |
Andreas Ruffing, Thomas Deck, Martin Schlichenmaier
|
alg-geom/9206001
|
Linear orbits of smooth plane curves
|
The group PGL(3) of linear transformations of the projective plane acts
naturally on the projective space parametrizing curves of a given degree. In
this note we begin the study of the orbits of smooth curves under this action:
we construct a resolution of the closure of the orbit of a given curve, and we
use it to compute its degree. This turns out to depend only on the degree of
the curve, the order of its automorphism group, and on the number and type of
its flexes. This paper will appear on the Journal of Algebraic Geometry.
| 1992-06-02
| 2012-04-10
|
[
"alg-geom",
"math.AG"
] |
Paolo Aluffi, Carel Faber
|
alg-geom/9205007
|
On the Tangent Space to the Universal Teichmuller Space
|
We find a remarkably simple relationship between the following two models of
the tangent space to the Universal Teichm\"uller Space: (1) The real-analytic
model consisting of Zygmund class vector fields on the unit circle; (2) The
complex-analytic model comprising 1-parameter families of schlicht functions on
the exterior of the unit disc which allow quasiconformal extension. Indeed, the
Fourier coefficients of the vector field in (1) turn out to be essentially the
same as (the first variations of) the corresponding power series coefficients
in (2). These identities have many applications; in particular, to conformal
welding, to the almost complex structure of Teichm\"uller space, to study of
the Weil-Petersson metric, to variational formulas for period matrices, etc.
These utilities are explored.
| 1992-05-22
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Subhashis Nag
|
alg-geom/9205006
|
Upper Bounds for the Betti Numbers of a given Hilbert Function
|
From a Macaulay's paper it follows that a lex-segment ideal has the greatest
number of generators (the 0-th Betti number $\b_0$) among all the homogeneous
ideals with the same Hilbert function. In this paper we prove that this fact
extends to every Betti number, in the sense that all the Betti numbers of a
minimal free resolution of a lex segment ideal are bigger than or equal to the
ones of any homogeneous ideal with the same Hilbert function.
| 1992-05-19
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Anna Maria Bigatti
|
alg-geom/9205005
|
Linear orbits of d-tuples of points in P^1
|
The group PGL(2) of linear transformations of the projective line acts
naturally on the d-dimensional projective space P^d parametrizing
configurations (`d-tuples') of points on the line. In this note we are
concerned with the orbits of this action of PGL(2) on P^d. The closure of each
orbit is a projective subvariety of P^d of which we determine the degree, the
`boundary'--i.e., the complement of an orbit in its closure--, and the
multiplicity at points of the boundary. These results are used to provide a
complete classification of the non-singular orbit closures, and criteria for an
orbit closure to be non-singular in codimension 1.
| 1992-05-12
| 2012-04-10
|
[
"alg-geom",
"math.AG"
] |
Paolo Aluffi, Carel Faber
|
alg-geom/9205004
|
Notes on Kodaira energies of polarized varieties
|
The Kodaira energy of a polarized manifold (M,L) is defined by
\kappa\epsilon(M,L)=-Inf{t\in Q|\kappa(K+tL)\ge 0}. Here we propose a couple of
conjectures and announce several partial results. 3-dimensional cases are
mainly considered. A hard copy is available on request to the author.
| 1992-05-08
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Takao Fujita
|
alg-geom/9205003
|
Chern classes and degenerations of hypersurfaces and their lines
|
We study limiting lines on degenerations of generic hypersurfaces in $P^n$.
| 1992-05-07
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Xian Wu
|
alg-geom/9205002
|
Cohomology, Symmetry, and Perfection
|
One of the aims of this paper is to better explain the philosophy behind the
computations in [E.Bifet, C.De Concini,C.Procesi Cohomology of Regular
Embeddings ] and to place them in a wider conceptual setting. Another aim of
the paper is to outline in the last section an ``equivariant'' approach to some
key results in the theory of toric varieties. The text of the first three
sections follows closely a talk delivered at the University of Copenhagen in
July 1989 on the occasion of the Zeuthen Symposium. This paper is dedicated to
the memory of my friend Pere Menal and will appear in the Fall 1992 issue,
dedicated to his memory, of Publicacions Matem\`atiques, Universitat Aut\`onoma
de Barcelona.
| 1992-05-04
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Emili Bifet
|
alg-geom/9205001
|
Report on the Torsion of the Differential Module of an algebraic Curve
|
There is a conjecture, that the torsionfreeness of the module of
differentials in a point of an algebraic or algebroid curve should imply that
the curve is non singular at that point. A report on the main results is given.
| 1992-05-03
| 2008-02-03
|
[
"alg-geom",
"math.AC",
"math.AG"
] |
Robert W. Berger
|
alg-geom/9204001
|
Weierstrass Gap Sequence at Total Inflection Points of Nodal Plane
Curves
|
Let $\Gamma$ be a plane curve of degree $d$ with $\delta$ ordinary nodes and
no other singularities. If $P$ is a smooth point on $\Gamma$ then the
Weierstrass gap sequence at $P$ is considered as that at the corresponding
point on the normalization of $\Gamma$. A smooth point $P\in\Gamma$ is called a
total inflection point if $i(\Gamma ,T;P)=d$ where $T$ is the tangent line to
$\Gamma$ at $P$. There are many possible Weierstrass gap sequences at total
inflection points. Our main results are: Among them (1) There exists a pair
$(P,\Gamma )$ such that the gap sequence at $P$ is the minimal (in the sense of
weight). (2) There exists a pair $(P,\Gamma )$ such that the gap sequence at
$P$ is the maximal (resp. up to 1 maximal). And we characterize these cases in
the sense of location of nodes.
| 1992-04-02
| 2015-06-30
|
[
"alg-geom",
"math.AG"
] |
Marc Coppens and Takao Kato
|
alg-geom/9203005
|
Homotopy groups of the complements to singular hypersurfaces,II
|
The homotopy group $\pi_{n-k} ({\bf C}^{n+1}-V)$ where $V$ is a hypersurface
with a singular locus of dimension $k$ and good behavior at infinity is
described using generic pencils. This is analogous to the van Kampen procedure
for finding a fundamental group of a plane curve. In addition we use a certain
representation generalizing the Burau representation of the braid group. A
divisibility theorem is proven that shows the dependence of this homotopy group
on the local type of singularities and behavior at infinity. Examples are given
showing that this group depends on certain global data in addition to local
data on singularities.
| 1992-03-24
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
A.Libgober
|
alg-geom/9203002
|
Prym Varieties and Integrable Systems
|
A new relation between Prym varieties of arbitrary morphisms of algebraic
curves and integrable systems is discovered. The action of maximal commutative
subalgebras of the formal loop algebra of GL(n) defined on certain
infinite-dimensional Grassmannians is studied. It is proved that every
finite-dimensional orbit of the action of traceless elements of these
commutative Lie algebras is isomorphic to the Prym variety associated with a
morphism of algebraic curves. Conversely, it is shown that every Prym variety
can be realized as a finite-dimensional orbit of the action of traceless
diagonal elements of the formal loop algebra, which defines the multicomponent
KP system.
| 1992-03-20
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Yingchen Li and Motohico Mulase
|
alg-geom/9203004
|
On the Abel-Jacobi Map for Divisors of Higher Rank on a Curve
|
The aim of this paper is to present an algebro-geometric approach to the
study of the geometry of the moduli space of stable bundles on a smooth
projective curve defined over an algebraically closed field $k$, of arbitrary
characteristic. This establishes a bridge between the arithmetic approach of
Harder, Narasimhan et al. and the gauge group approach of Atiyah and Bott. One
of the basic ideas is to consider a notion of divisor of higher rank and a
suitable Abel-Jacobi map generalizing the classical notions in rank one.
| 1992-03-19
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Emili Bifet, Franco Ghione and Maurizio Letizia
|
alg-geom/9203003
|
Computing the Cohomological Brauer Group of a Toric Variety
|
The purpose of this article is to show how one might compute the \'etale
cohomology groups $H^p_{\acute{e}t}(X,G_m)$ in degrees $p=0$, $1$ and $2$ of a
toric variety $X$ with coefficients in the sheaf of units. The method is to
reduce the computation down to the problem of diagonalizing a matrix with
integral coefficients. The procedure outlined in this article has been fully
implemented by the author as a program written in the ``C'' programming
language.
| 1992-03-18
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Timothy J. Ford
|
alg-geom/9203001
|
Exceptional linear systems on curves on Enriques surfaces
|
The main purpose in this paper is to study the gonality, the Clifford index
and the Clifford dimension on linearly equivalent smooth curves on Enriques
surfaces. The method is similar to techniques of M.Green $\&$ R.Lazarsfeld and
G.Pareschi.
| 1992-03-05
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Severinas Zube
|
alg-geom/9202028
|
Complex Divisors on Algebraic Curves and Some Applications to String
Theory
|
These are notes of a talk to the International Conference on Algebra in honor
of A. I. Mal'tsev, Novosibirsk, USSR, 1989 (to appear in Contemporary
Mathematics). The concept of a divisor with complex coefficients on an
algebraic curve is introduced. We consider families of complex divisors, or,
equivalently, families of invertible sheaves and define Arakelov-type metrics
on some invertible sheaves produced from them on the base. We apply this
technique to obtain a formula for the measure on the moduli space that gives
tachyon correlators in string theory.
| 1992-02-27
| 2008-02-03
|
[
"alg-geom",
"hep-th",
"math.AG"
] |
A. A. Voronov
|
alg-geom/9202027
|
Cohomological and Cycle-theoretic connectivity
|
One of the themes in algebraic geometry is the study of the relation between
the ``topology'' of a smooth projective variety and a (``general'') hyperplane
section. Recent results of Nori produce cohomological evidence for a conjecture
that a general hypersurface of sufficently large degree should have no
``interesting'' cycles. We compute precise bounds for these results and show by
example that there are indeed interesting cycles for degrees that are not high
enough. In a different direction Esnault, Nori and Srinivas have shown
connectivity for intersections of small multidegree. We show analogous
cycle-theoretic connectivity results.
| 1992-02-26
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Kapil H. Paranjape
|
alg-geom/9202026
|
Picard-Fuchs equations and mirror maps for hypersurfaces
|
We describe a strategy for computing Yukawa couplings and the mirror map,
based on the Picard-Fuchs equation. (Our strategy is a variant of the method
used by Candelas, de la Ossa, Green, and Parkes in the case of quintic
hypersurfaces.) We then explain a technique of Griffiths which can be used to
compute the Picard-Fuchs equations of hypersurfaces. Finally, we carry out the
computation for four specific examples (including quintic hypersurfaces,
previously done by Candelas et al.). This yields predictions for the number of
rational curves of various degrees on certain hypersurfaces in weighted
projective spaces. Some of these predictions have been confirmed by classical
techniques in algebraic geometry.
| 1992-02-26
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
David R. Morrison
|
alg-geom/9202024
|
Sur la cohomologie de certains espaces de modules de fibr\'es vectoriels
|
Let M be a moduli space of stable vector bundles on a curve with rank and
degree fixed and coprime. We give a simple proof that the rational cohomology
of M is generated by the Kunneth components of the Chern classes of the
universal bundle. The proof applies also to some moduli spaces of vector
bundles over higher-dimensional varieties.
| 1992-02-21
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
A. Beauville
|
alg-geom/9202025
|
The Singularities of the parameter surface of a minimal elliptic
threefold
|
Let f : X -> S be any elliptic fibration. If X has dimension 3 and is not
uniruled, then X has a minimal model (with terminal singularities) [Mori]. In
earlier work we have shown that there exists a birationally equivalent elliptic
fibration p: Y -> T such that Y is minimal and a multiple of K_Y can be
expressed as the pullback of a divisor from T. Moreover T has at worst quotient
singularities; it is not difficult to find examples where T is actually
singular. In this paper we describe the singularities of this parameter surface
T in the case of no multiple fibers. Although T is not uniquely determined by
the birational equivalence class of the fibration, any two such T are related
by a particular kind of birational map.
| 1992-02-21
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
A. Grassi
|
alg-geom/9202021
|
Grobner bases and extension of scalars
|
This paper studies the behavior of Grobner bases with respect to extensions
of scalars. We prove that an extension of scalars commutes with taking Grobner
bases iff the extension is flat. We consider what information can be deduced
about fibers of a family, from the Grobner basis of the defining ideal of the
family itself. This information can be used to construct algorithms, such as to
find locii over which a map is finite, or an isomorphism.
| 1992-02-20
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Dave Bayer, Andre Galligo, Mike Stillman
|
alg-geom/9202022
|
Classical Polylogarithms
|
This paper is an introduction to classical polylogarithms and is an expanded
version of a talk given by the author at the Motives conference. Topics covered
include, monodromy; the polylogarithm local systems; Bloch's constructions of
regulators using the dilogarithm; polylog locals systems as variations of mixed
Hodge structre; the polylogarithm quotient of the fundamental group of C -
{0,}. It is intended as background for understanding recent work of Beilinson,
Deligne, and Goncharov.
| 1992-02-20
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Richard Hain
|
alg-geom/9202020
|
Disproving Hibi's Conjecture with CoCoA or Projective Curves with bad
Hilbert Functions
|
In this paper we show how to combine different techniques from Commutative
Algebra and a systematic use of a Computer Algebra System (in our case mainly
CoCoA) in order to explicitly construct Cohen-Macaulay domains, which are
standard $k$-algebras and whose Hilbert function is ``bad". In particular we
disprove a well-known conjecture by Hibi.
| 1992-02-20
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
G. Niesi, L. Robbiano
|
alg-geom/9202023
|
Regulators and characteristic classes of flat bundles
|
This is a substantial revision of the older version of this paper. The main
result of the old version (the equality, up to a factor of 2 of the Beilinson
and Borel regulators) is now a conjecture. The main results give equality of
Beilinson chern classes and Cheeger-Simons-Chern classes in various situations
such as for flat bundles over quasi projective varieties. We also prove the
equality (up to a factor of two) of the Borel regulator element and the
universal Cheeger-Simons Chern class.
| 1992-02-20
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Johan Dupont, Richard Hain and Steven Zucker
|
alg-geom/9202018
|
Arithmetically Cohen-Macaulay Curves cut out by Quadrics
|
Addressing a question of M. Stillman, it had been shown by Ein, Eisenbud, and
the author that in a projective space of dimension at most 5, every
arithmetically Cohen-Macaulay curve which is cut out by quadrics scheme-
theoretically also has its homogeneous ideal generated by quadrics. In this
note it is shown that this is not the case in higher dimensional spaces.
| 1992-02-19
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Sheldon Katz
|
alg-geom/9202019
|
The cohomological Brauer group of a toric variety
|
Toric varieties are a special class of rational varieties defined by
equations of the form {\it monomial = monomial}. For a good brief survey of the
history and role of toric varieties see [10]. Any toric variety $X$ contains a
cover by affine open sets described in terms of arrangements (called fans) of
convex bodies in $\Bbb R^r$. The coordinate rings of each of these affine open
sets is a graded ring generated over the ground field by monomials. As a
consequence, toric varieties provide a good context in which cohomology can be
calculated. The purpose of this article is to describe the second \'etale
cohomology group with coefficients in the sheaf of units of any toric variety
$X$. This is the so-called cohomological Brauer group of $X$.
| 1992-02-19
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Frank DeMeyer, Tim Ford, and Rick Miranda
|
alg-geom/9202016
|
Congruences for real algebraic curves on an ellipsoid
|
The problem of arrangement of a real algebraic curve on a real algebraic
surface is related to the 16th Hilbert problem. We prove in this paper new
restrictions on arrangement of nonsingular real algebraic curves on an
ellipsoid. These restrictions are analogues of Gudkov-Rokhlin,
Gudkov-Krakhnov-Kharlamov, Kharlamov-Marin congruences for plane curves (see
e.g. \cite{V} or \cite{V1}). To prove our results we follow Marin approach
\cite{Marin} that is a study of the quotient space of a surface under the
complex conjugation. Note that the Rokhlin approach \cite{R} that is a study of
the 2-sheeted covering of the surface branched along the curve can not be
directly applied for a proof of Theorem \ref{Rokhlin} since the homology class
of a curve of Theorem \ref{Rokhlin} can not be divided by 2 hence such a
covering space does not exist.
| 1992-02-18
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
G.Mikhalkin
|
alg-geom/9202017
|
Extensions of Rokhlin congruence for curves on surfaces
|
The subject of this paper is the problem of arrangement of a real nonsingular
algebraic curve on a real non-singular algebraic surface. This paper contains
new restrictions on this arrangement extending Rokhlin and
Kharlamov-Gudkov-Krakhnov congruences for curves on surfaces.
| 1992-02-18
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
G.Mikhalkin
|
alg-geom/9202015
|
Note on curves in a Jacobian
|
For a curve C, viewed as a cycle in its Jacobian, we study its image n_*C
under multiplication by n on JC. We prove that the subgroup generated by these
cycles, in the Chow group modulo algebraic equivalence, has rank at most d-1,
where d is the gonality of C. We also discuss some general facts on the action
of n_* on the Chow groups.
| 1992-02-17
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Elisabetta Colombo and Bert van Geemen
|
alg-geom/9202014
|
Degenerations of generalized KNN algebras on tori
|
Degenerations of Lie algebras of meromorphic vector fields on elliptic curves
(i.e. complex tori) which are holomorphic outside a certain set of points
(markings) are studied. By an algebraic geometric degeneration process certain
subalgebras of Lie algebras of meromorphic vector fields on P^1 the Riemann
sphere are obtained. In case of some natural choices of the markings these
subalgebras are explicitly determined. It is shown that the number of markings
can change.
AMS subject classification (1991): 17B66, 17B90, 14F10, 14H52, 30F30, 81T40
| 1992-02-17
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Martin Schlichenmaier
|
alg-geom/9202013
|
Deformations of Semi-Euler Characteristics
|
(Generalizes theorem of Atiyah and Mumford.)
| 1992-02-14
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
George R. Kempf
|
alg-geom/9202012
|
Cohomology of coherent sheaves on a proper scheme
|
(Makes a Gamma-acylic coherent resolution of a coherent sheaf on a projection
scheme.)
| 1992-02-14
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
George R. Kempf
|
alg-geom/9202011
|
The Geometry and Arithmetic of Elliptic Surfaces
|
We survey some aspects of the theory of elliptic surfaces and give some
results aimed at determining the Picard number of such a surface. For the
surfaces considered, this will be equivalent to determining the Mordell-Weil
rank of an elliptic curve defined over a function field in one variable. An
interesting conjecture concerning Galois actions on the relative de~Rham
cohomology of these surfaces is discussed.
| 1992-02-14
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Peter F. Stiller
|
alg-geom/9202010
|
Another Relation Between Approaches to the Schottky Problem
|
The recent extensive work on different approaches to the Schottky problem has
produced marked progress on several fronts. At the same time, it has become
apparent that there exist very close connections between the various
characterizations of Jacobian varieties described in Mumford's classic lectures
{\it Curves and Their Jacobians\/}. Until now, the approach via double
translation manifolds has seemed to be quite different from other approaches to
the Schottky problem. The purpose of this paper is to bring this last approach
``into the fold'' as it were, and to show precisely how it relates to
characterizations of Jacobians based on trisecants and flexes of the Kummer
variety, and the K.P. equation.
| 1992-02-13
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
John B. Little
|
alg-geom/9202009
|
On a Grauert-Riemenschneider vanishing theorem for Frobenius split
varieties in characteristic p
|
This paper is about sheaf cohomology for varieties (schemes) in
characteristic $p>0$. We assume the presence of a Frobenius splitting. (See
V.B. Mehta and A. Ramanathan, Frobenius splitting and cohomology vanishing for
Schubert varieties, Annals of Math. 122 (1985), 27--40). The main result is
that a non-zero higher direct image under a proper map of the ideal sheaf of a
compatibly Frobenius split subvariety can not have a support whose inverse
image is contained in that subvariety. Earlier vanishing theorems for Frobenius
split varieties were based on direct limits and Serre's vanishing theorem, but
our theorem is based on inverse limits and Grothendieck's theorem on formal
functions. The result implies a Grauert--Riemenschneider type theorem.
| 1992-02-13
| 2009-10-22
|
[
"alg-geom",
"math.AG"
] |
V. B. Mehta and Wilberd van der Kallen
|
alg-geom/9202007
|
The algebraic de Rham theorem for toric varieties
|
On an arbitrary toric variety, we introduce the logarithmic double complex,
which is essentially the same as the algebraic de Rham complex in the
nonsingular case, but which behaves much better in the singular case. Over the
field of complex numbers, we prove the toric analog of the algebraic de Rham
theorem which Grothendieck formulated and proved for general nonsingular
algebraic varieties re-interpreting an earlier work of Hodge-Atiyah. Namely,
for a finite simplicial fan which need not be complete, the complex cohomology
groups of the corresponding toric variety as an analytic space coincide with
the hypercohomology groups of the single complex associated to the logarithmic
double complex. They can then be described combinatorially as Ishida's
cohomology groups for the fan. We also prove vanishing theorems for Ishida's
cohomology groups. As a consequence, we deduce directly that the complex
cohomology groups vanish in odd degrees for toric varieties which correspond to
finite simplicial fans with full-dimensional convex support. In the particular
case of complete simplicial fans, we thus have a direct proof for an earlier
result of Danilov and the author.
| 1992-02-12
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Tadao Oda
|
alg-geom/9202008
|
On irregular links at infinity of algebraic plane curves
|
We give two proofs of a conjecture of the first author (Inv. Math. 98, 1989)
that a reduced algebraic plane curve is regular at infinity if and only if its
link at infinity is a regular toral link. This conjecture has also been proved
by Ha H.~V. using Lojasiewicz numbers at infinity. Our first proof uses the
polar invariant and the second proof uses linear systems of plane curve
singularities. The second approach (based on a paper in preparation) also
proves a stronger conjecture (loc. cit.) describing topologically the regular
link at infinity associated with an irregular link at infinity.
| 1992-02-12
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Walter D. Neumann and Le Van Thanh
|
alg-geom/9202005
|
On the difference between real and complex arrangements
|
Let $B$ be an arrangement of linear complex hyperplanes in $C^d$. Then a
classical result by Orlik \& Solomon asserts that the cohomology algebra of the
complement can be constructed from the combinatorial data that are given by the
intersection lattice.
If $B'$ is, more generally, a $2$-arrangement in $R^{2d}$ (an arrangement of
real subspaces of codimension $2$ with even-dimensional intersections), then
the intersection lattice still determines the cohomology {\it groups} of the
complement, as was shown by Goresky \& MacPherson. We prove, however, that for
$2$-arrangements the cohomology {\it algebra} is not determined by the
intersection lattice. It encodes extra information on sign patterns, which can
be computed from determinants of linear relations or, equivalently, from
linking coefficients in the sense of knot theory. This also allows us (in the
case $d=2$) to identify arrangements with the same lattice but different
fundamental groups.
| 1992-02-11
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
G\"unter M. Ziegler
|
alg-geom/9202006
|
Twistors, Kaehler Manifolds, and Bimeromorphic Geometry II
|
Using examples of compact complex 3-manifolds which arise as twistor spaces,
we show that the class of compact complex manifolds bimeromorphic to K\"ahler
manifolds is not stable under small deformations of complex structure.
| 1992-02-11
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Claude LeBrun and Yat-Sun Poon
|
alg-geom/9202004
|
Mirror symmetry and rational curves on quintic threefolds: a guide for
mathematicians
|
We give a mathematical account of a recent string theory calculation which
predicts the number of rational curves on the generic quintic threefold. Our
account involves the interpretation of Yukawa couplings in terms of variations
of Hodge structure, a new $q$-expansion principle for functions on the moduli
space of Calabi-Yau manifolds, and the ``mirror symmetry'' phenomenon recently
observed by string theorists.
| 1992-02-10
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
David R. Morrison
|
alg-geom/9202003
|
Complex Contact Threefolds and Their Contact Curves
|
A complex contact threefold is a threefold with a two-dimensional
non-integrable holomorphic distribution. A contact curve on a contact threefold
is an integrable curve of the distribution. This work was inspired by two
papers of Bryant, in which he used complex contact geometry to study
superminimal surfaces in four-sphere and to investigate exotic holonomies. The
present paper is devoted to systematical studies of contact threefold and
contact curves on them. We generalize a result of Bryant and answer a question
of his.
| 1992-02-07
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Yun-Gang Ye
|
alg-geom/9202001
|
Rational Curves on Calabi-Yau Threefolds
|
The point is to compare the mathematical meaning of the ``number of rational
curves on a Calabi-Yau threefold'' to the meaning ascribed to the same notion
by string theorists.
| 1992-02-05
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Sheldon Katz
|
alg-geom/9202002
|
Gorenstein Threefold Singularities with Small Resolutions via Invariant
Theory for Weyl Groups
|
We classify simple flops on smooth threefolds, or equivalently, Gorenstein
threefold singularities with irreducible small resolution. There are only six
families of such singularities, distinguished by Koll{\'a}r's {\em length}
invariant. The method is to apply invariant theory to Pinkham's construction of
small resolutions. As a by-product, generators of the ring of invariants are
given for the standard action of the Weyl group of each of the irreducible root
systems.
| 1992-02-05
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Sheldon Katz and David R. Morrison
|
astro-ph/9212006
|
Two Populations and Models of Gamma Ray Bursts
|
Gamma-ray burst statistics are best explained by a source population at
cosmological distances, while spectroscopy and intensity histories of some
individual bursts imply an origin on Galactic neutron stars. To resolve this
inconsistency I suggest the presence of two populations, one at cosmological
distances and the other Galactic. I build on ideas of Shemi and Piran (1990)
and of M\'esz\'aros and Rees (1993) involving the interaction of fireball
debris with surrounding clouds to explain the observed intensity histories in
bursts at cosmological distances. The distances to the Galactic population are
undetermined because they are too few to affect the statistics of intensity and
direction; I explain them as resulting from magnetic reconnection in neutron
star magnetospheres.
| 1992-12-31
| 2015-06-24
|
[
"astro-ph"
] |
J. I. Katz
|
astro-ph/9212005
|
The Escape of Gravitational Radiation from the Field of Massive Bodies
|
We consider a compact source of gravitational waves of frequency $\omega$, in
or near a massive spherically symmetric distribution of matter or a black hole.
Recent calculations have led to apparently contradictory results for the
influence of the massive body on the propagation of the waves. We show here
that the results are in fact consistent and in agreement with the ``standard''
viewpoint in which the high frequency compact source produces the radiation as
if in a flat background, and the background curvature affects the propagation
of these waves.
| 1992-12-23
| 2010-11-30
|
[
"astro-ph",
"gr-qc"
] |
Richard H. Price, Jorge Pullin and Prasun Kundu
|
astro-ph/9212004
|
Recent advances in extended inflationary cosmology
|
Extended inflation is a promising new approach to implementing the
inflationary universe scenario. This paper reviews recent advances including a
new, more robust mechanism for ending extended inflation, a new prediction for
the density fluctuation spectrum generated by extended inflation, and the
discovery that extended inflation can produce gravitational waves that can
significantly add to the cosmic background anisotropy. Invited Talk at the
Journees Relativistes, Amsterdam, May 14-16, 1992
| 1992-12-16
| 2010-04-06
|
[
"astro-ph"
] |
Paul J. Steinhardt
|
astro-ph/9212003
|
Gravity's rainbow
|
Could COBE DMR be detecting the imprint from a spectrum of gravitational
waves generated during inflation? The conventional inflationary prediction had
been that the cosmic microwave anisotropy is dominated by energy density
fluctuations generated during inflation and that the gravitational waves
contribute negligibly. In this paper, we report on recent work (in
collaboration with R. Davis, H. Hodges, and M. Turner) that has shown that the
conventional wisdom may be wrong; specifically, gravitational waves may
dominate the anisotropy in inflationary models where the spectrum of
perturbations deviates significantly from scale invariance (e.g., extended and
power-law inflation models and extreme versions of chaotic inflation). If
gravitational waves do dominate at the large-angular scales measured by COBE
DMR, the expectation and interpretation of anisotropies on small-angular scales
is profoundly altered. Invited Paper for Proceedings of the Journees
Relativistes, Amsterdam, May 14-16, 1992
| 1992-12-16
| 2009-09-15
|
[
"astro-ph"
] |
George F. Smoot and Paul J. Steinhardt
|
astro-ph/9212002
|
Structure in a Loitering Universe
|
We study the formation of structure for a universe that undergoes a recent
loitering phase. We compare the nonlinear mass distribution to that in a
standard, matter dominated cosmology. The statistical aspects of the clustered
matter are found to be robust to changes in the expansion law, an exception
being that the peculiar velocities are lower by a factor of $\sim 3$ in the
loitering model. Further, in the loitering scenario, nonlinear growth of
perturbation occurs more recently ($z\sim 3-5$) than in the matter dominated
case. Differences in the high redshift appearances of the two models will
result but observable consequences depend critically on the chosen form, onset
and duration of the loitering phase.
| 1992-12-10
| 2009-10-22
|
[
"astro-ph",
"hep-ph"
] |
Hume A. Feldman and August E. Evrard
|
astro-ph/9212001
|
A rotating black hole in the Galactic Center
|
Recent observations of Sgr A* give strong constraints for possible models of
the physical nature of Sgr A* and suggest the presence of a massive black~hole
with M<2 10^6 M_sun surrounded by an accretion disk which we estimate to
radiate at a luminosity of <7 10^5 L_sun. We therefore calculate the appearance
of a standard accretion disk around a Kerr hole in Sgr A* following from
general relativity and a few fundamental assumptions. Effective temperature and
luminosity of the disk spectra do not depend on the unknown viscosity mechanism
but instead are quite sensitive to variations of intrinsic parameters: the
mass, the accretion rate, the angular momentum of the accreting hole and the
inclination angle. A radiation field of L~7 10^4 - 7 10^5 L_sun and T_eff ~ 2-4
10^4 K can be ascribed to a rapidly rotating Kerr~hole (a>0.9) accreting
10^-8.5 - 10^-7 M_sun/yr at a black~hole mass of M=2 10^6 M_sunseen almost edge
on. A low mass black hole of M<10^3 M_sun seems to be very unlikely. We provide
a ``Hertzsprung-Russell diagram for black holes'' together with simple scaling
laws to provide an easy-to-handle test for the black hole model.
| 1992-12-07
| 2011-05-23
|
[
"astro-ph"
] |
Heino Falcke, Peter L. Biermann, Wolfgang J. Duschl and Peter G.
Mezger
|
astro-ph/9211014
|
On the General Properties of Matter
|
By means of a general classification of the different kinds of matter of
nature form a chain from the world of the subatomic particles to the large
bodies of the universe, the galaxies. Then, it proposes a new baryonic force
for the universe that is the fifth force which has been proposed in the
literature. It explains the universal expansion itself and shows why the
expansion must be slowing down at present. This force depends on the ratio of
the number of neutrons to the number of protons. Its potential for the Universe
is a well. At the bottom of the well the potential is of the form $kx^2$, where
$x$ is the separation among the bodies under consideration. It is suggested
that Nature has six fundamental forces which are unified in pairs and,
therefore, reduced to three at $t=0$. The condition for having a closed
universe is found. This new force, called superweak force in this paper,
explains also the evolution of galaxies and shows how the arms of spiral
galaxies(including barred spirals) are formed. The variation of the Hubble
constant with time is shown. It is shown that quarks are formed of prequarks
which may be the true elementary particles. The paper also gives a physical
explanation for quark confinement. The energies of baryon states are calculated
in a simple manner. The paper proposes the existence of four more bosons, one
for the superweak interaction and three for the superstrong interaction. The
six figures will be sent by mail upon request.
| 1992-11-30
| 2007-05-23
|
[
"astro-ph"
] |
Mario Everaldo de Souza (Departamento de Fisica, Universidade Federal
de Sergipe, Aracaju, Brazil)
|
astro-ph/9211013
|
Particle Astrophysics after COBE: Blois92 Summary Talk
|
The IV Rencontres de Blois, on Particle Astrophysics, held at the Ch\^ateau
de Blois, June 15-20, 1992, was a meeting well-timed for a reconsideration of
the issues in particle astrophysics in the light of the COBE discovery of the
cosmic microwave background (CMB) fluctuations. This is a summary of what I
thought were the most interesting things discussed at Blois: (1) The
near-success of Cold Dark Matter (CDM) in predicting the COBE fluctuation
amplitude, which favors the hypothesis that structure formed in the universe
through gravitational collapse. (2) The indications that $\Omega\approx1$ and
that the power spectrum has a little more power on supercluster and larger
scales than CDM. These are suggested by the IRAS and CfA redshift surveys and
POTENT galaxy peculiar velocity analysis, and also by the COBE data. (3) The
consequent demise of CDM and the rise of hybrid schemes such as Cold+Hot Dark
Matter (C+HDM). (4) The possible implications for neutrino masses and mixings,
and for cosmology, of the recent results on solar neutrinos. (5) The first
discovery of TeV $\gamma$ rays from an extragalactic source, which was
announced at Blois. I also summarize here a number of the exciting ongoing and
planned experiments and observations discussed at Blois: CERN experiments on
$\nu_\mu \nu_\tau$ oscillations, which may be sufficiently sensitive to detect
the $\nu_\tau$ if
| 1992-11-20
| 2007-05-23
|
[
"astro-ph",
"hep-ph"
] |
Joel R. Primack
|
astro-ph/9211010
|
Gamma-Ray Bursts and Neutron Star Mergers - Possibly the Strongest
Explosions in the Universe
|
$\gamma$-ray bursts have baffled theorists ever since their accidental
discovery at the sixties. We suggest that these bursts originate in merger of
neutron star binaries, taking place at cosmological distances. These mergers
release $\approx 10^{54}ergs$, in what are possibly the strongest explosions in
the Universe. If even a small fraction of this energy is channeled to an
electromagnetic signal it will be detected as a grbs. We examine the virtues
and limitations of this model and compare it with the recent Compton \g-ray
observatory results.
| 1992-11-17
| 2009-10-22
|
[
"astro-ph"
] |
Tsvi Piran
|
astro-ph/9211011
|
A Possible Solution to the Horizon Problem: The Mad Era for Massless
Scalar Theories of Gravity
|
Extensions of Einstein gravity which allow the gravitational constant $G$ to
change with time as the universe evolves may provide a resolution to the
horizon problem without invoking a period of vacuum domination and without the
subsequent entropy violation. In a cosmology for which the gravitational
constant is not in fact constant, the universe may be older at a given
temperature than in a standard Hot Big Bang universe; thus, larger regions of
space could have come into causal contact at that temperature. This opens the
possibility that large regions became smooth at some high temperature without
violating causality. The extra aging of the universe can be accomplished by an
early period with a large Planck mass, a period we call the MAD era (Modified
Aging era or the Massively Aged and Detained era). We discuss in this paper
theories of gravity in which the gravitational constant is replaced with a
function of a scalar field. However, this resolution to the smoothness problem
| 1992-11-17
| 2009-10-22
|
[
"astro-ph",
"gr-qc",
"hep-ph"
] |
Janna J Levin and Katherine Freese
|
astro-ph/9211012
|
On the rotation of polarization by a gravitational lens
|
It is proved that the field of a gravitational lens induces no rotation in
the polarization vector of electromagnetic radiation, in agreement with the
previous literature, but with a different approach. The result is generalized
to the case of less conventional gravitational lenses (static cosmic strings
and gravitational waves).
| 1992-11-17
| 2007-05-23
|
[
"astro-ph"
] |
Valerio Faraoni
|
astro-ph/9211009
|
Fireballs in the Galactic Halo and $\gamma$-Ray Bursts
|
If gamma ray burst sources are in the galactic halo they inevitably involve a
creation of an opaque pair plasma fireball, just like in cosmological sources.
We find that the typical physical conditions in a galactic halo fireball are:
optical depth $\ap 10^8$, thermal energy $\ap 100 KeV$, maximal relativstic
expansion $\G \ap 300 $ and a maximal baryonic load of $\ap 10^{-15} M_\odot$.
This does not rule out galctic halo models but it poses an addtional severe
constraint on all such sources. A comparison of these conditions with the
physical conditions at cosmological fireballs reveal that galactic halo
fireballs are less favorable than cosmological ones as sources of gamma ray
bursts.
| 1992-11-13
| 2009-10-22
|
[
"astro-ph"
] |
Tsvi Piran and Amotz Shemi
|
astro-ph/9211008
|
The Mad Era: A Possible New Resolution to the Horizon, Flatness, and
Monopole Problems
|
A cosmology with a dynamical Planck mass $m_{pl}$ is shown to solve the
horizon and monopole problems (and possibly flatness) if there is an early MAD
(modified aging) era where the universe becomes older than in the standard
model as a result of a large $m_{pl}$: the causality condition is $m_{pl}(T_c)/
m_{pl}(T_o) \gta T_c/T_o$ ($T_c$ is some high temperature while $T_o = 2.74K$.)
Unlike inflation, there is no period of vacuum domination nor any entropy
violation. We study: a) bare scalar theories of gravity, b) self-interacting
models, and c) bare theories with a phase transition in the matter sector.
| 1992-11-10
| 2007-05-23
|
[
"astro-ph",
"gr-qc",
"hep-ph"
] |
Katherine Freese and Janna J Levin
|
astro-ph/9211007
|
Generalized Einstein Theory on Solar and Galactic Scales
|
We study a generalized Einstein theory with the following two criteria:{\it
i}) on the solar scale, it must be consistent with the classical tests of
general relativity, {\it ii}) on the galactic scale, the gravitational
potential is a sum of Newtonian and Yukawa potentials so that it may explain
the flat rotation curves of spiral galaxies. Under these criteria, we find that
such a generalized Einstein action must include at least one scalar field and
one vector field as well as the quadratic term of the scalar curvature.
| 1992-11-09
| 2010-11-01
|
[
"astro-ph",
"gr-qc"
] |
Masakatsu Kenmoku, Yuko Okamoto and Kazuyasu Shigemoto
|
astro-ph/9211006
|
The ($\log R_e$, $\mu_e$) Plane of Hot Stellar Systems
|
Two families of hot stellar systems, named {\it `ordinary'\/} and {\it
'bright'\/}, are identified in the ($\log R_e, \mu_e$) plane built with a
luminosity--limited sample of ellipticals and bulges of S0s and spirals of the
Virgo and Fornax clusters. This finding, based on {\it ad hoc\/} new
observations, is confirmed by a much larger set of literature data for
$\sim1500$ galaxies. The {\it `ordinary'\/} family is biparametric: $L_T\propto
I_e\,R_e^2$; its members are fainter that $M_B\simeq-19.3$ and smaller than
$\re\simeq3$ kpc (whatever $M_B$ is). The {\it 'bright'\/} family is
uniparametric ($\mu_e$ depends on $R_e$ alone) and hosts brightest cluster
members and QSO parent galaxies. We show that the segregation in the ($\log
R_e, \mu_e$) plane has an important counterpart in the behavior of various
physical parameters, which is markedly different for galaxies smaller ({\it
`ordinary'\/} family) and larger ({\it 'bright'\/} family) than $R_e=3$ kpc.
| 1992-11-09
| 2007-05-23
|
[
"astro-ph"
] |
Massimo Capaccioli, Nicola Caon and Mauro D'Onofrio
|
astro-ph/9211005
|
Centri`fugal' Force around a Black Hole
|
Besides having some very interesting perturbatively unstable orbits, it seems
that for a Schwarzschild black hole, below $r=3M$, the force always increases
inward with increasing angular momentum. Here this previously known result is
derived with greater simplicity, and a similar analysis is performed for black
holes with angular momentum and charge.
| 1992-11-08
| 2008-02-03
|
[
"astro-ph"
] |
A.Y.Shiekh
|
astro-ph/9211004
|
Gravitational Radiation from Colliding Vacuum Bubbles: Envelope
Approximation to Many-Bubble Collisions
|
We introduce an approximation to calculate the gravitational radiation
produced by the collision of true-vacuum bubbles that is simple enough to allow
the simulation of a phase transition by the collision of hundreds of bubbles.
This ``envelope approximation'' neglects the complicated ``overlap'' regions of
colliding bubbles and follows only the evolution of the bubble walls. The
approximation accurately reproduces previous results for the gravitational
radiation from the collision of two scalar-field vacuum bubbles. Using a bubble
nucleation rate given by $\Gamma = \Gamma_0 e^{\beta t}$, we simulate a phase
transition by colliding 20 to 200 bubbles; the fraction of vacuum energy
released into gravity waves is $E_{\rm GW}/E_{\rm vac} = 0.06(H/\beta)^2$ and
the peak of the spectrum occurs at $\omega_{\rm max}=1.6\beta$ ($H^2=8\pi G\rho
/3$ is the Hubble constant associated with the false-vacuum phase). The
spectrum is very similar to that in the two-bubble case, except that the
efficiency of gravity-wave generation is about five times higher, presumably
due to the fact that a given bubble collides with many others. Finally, we
consider two further ``statistical'' approximations, where the gravitational
radiation is computed as an incoherent sum over individual bubbles weighted by
the distribution of bubble sizes. These approximations provide reasonable
estimates of the gravitational-wave spectrum with far less computation.
| 1992-11-07
| 2008-11-26
|
[
"astro-ph",
"hep-ph"
] |
Arthur Kosowsky and Michael S. Turner
|
astro-ph/9211003
|
Evolution of Elliptical Galaxies: The Multiphase Model
|
We present a multiphase model for the evolution of elliptical galaxies.
Diffuse gas, molecular clouds, stars and remnants are taken into account.
Cloud--cloud collisions and stimulated processes are the main causes of star
formation. The occurrence of winds driven by Supernovae is considered, and the
evolution of the system is computed also after the first wind, allowing for
further star formation from the restored gas. The evolution of the abundances
of 15 elements or isotopes is followed with detailed stellar nucleosynthesis.
Stellar lifetimes are taken into account and a new IMF has been adopted. The
gas removal due to the Supernovae explosions depends on the galactic mass and
the presence of dark matter; the subsequent wind episodes are crucial to the
intergalactic gas enrichment. Good agreement is obtained for current SNs rates,
Star Formation Rate and gas masses when compared to the available data.
| 1992-11-07
| 2009-10-22
|
[
"astro-ph"
] |
Federico Ferrini, Bianca Maria Poggianti
|
astro-ph/9211002
|
Detection of brown dwarfs by the micro-lensing of unresolved stars
|
The presence of brown dwarfs in the dark galactic halo could be detected
through their gravitational lensing effect and experiments under way monitor
about one million stars to observe a few lensing events per year. We show that
if the photon flux from a galaxy is measured with a good precision, it is not
necessary to resolve the stars and besides more events could be observed.
| 1992-11-04
| 2007-05-23
|
[
"astro-ph"
] |
Paul Baillon, Alain Bouquet, Yannick Giraud-H\'eraud and Jean Kaplan
|
astro-ph/9211001
|
A Burst of Speculation
|
Self-consistent models of gamma-ray burst source regions at 100 Kpc distance
are possible if the radiating plasma is confined to very thin sheets, and I
estimate parameters. Energy sources might be elastic (by starquakes) or
magnetic (by reconnection), but mechanisms remain obscure. I discuss a very
speculative model involving collisions between comets in a hypothetical inner
Oort cloud.
| 1992-11-03
| 2015-06-24
|
[
"astro-ph"
] |
J. I. Katz
|
astro-ph/9210007
|
Effect of Neutrino Heating on Primordial Nucleosynthesis
|
We have modified the standard code for primordial nucleosynthesis to include
the effect of the slight heating of neutrinos by $e^\pm$ annihilations. There
is a small, systematic change in the $^4$He yield, $\Delta Y \simeq +1.5\times
10^{-4}$, which is insensitive to the value of the baryon-to-photon ratio
$\eta$ for $10^{-10}\la \eta \la 10^{-9}$. We also find that the
baryon-to-photon ratio decreases by about 0.5\% less than the canonical factor
of 4/11 because some of the entropy in $e^\pm$ pairs is transferred to
neutrinos. These results are in accord with recent analytical estimates.
| 1992-10-31
| 2009-10-22
|
[
"astro-ph",
"hep-ph"
] |
B. Fields, S. Dodelson, M.S. Turner (U. Chicago/Fermilab)
|
astro-ph/9210006
|
On the Origin of the Galactic Magnetic Field
|
The galactic magnetic field is commonly supposed to be due to a dynamo acting
on some large scale seed field. A major difficulty with this idea is that
estimates of reasonable seed field strengths tend to be quite low, on the order
of $\sim10^{-20}$ gauss. Here we examine the contribution due to the flux
entrained in winds from protostars formed in the first dynamo e-folding time of
a galaxy's existence. Using a minimal estimate of a protostellar magnetic field
we find that if each protostar ejects a single current ring, sufficient to
maintain flux freezing in the wind, than the large scale average dipole field
from all such current rings will be at least 5 orders of magnitude larger than
previous seed field estimates. Allowing for a reasonable amount of magnetic
activity in protostars during an extended period of mass loss increases this to
a dipole seed field of $\sim10^{-12}$ gauss. For the purposes of producing a
seed field it is irrelevant whether or not this initial injection of flux takes
place in a newly formed galactic disk, or in star forming proto-galactic
clouds. The compression of this dipole field into a thin disk will lead to a
large scale $B_r\sim 10^{-10.5}$ gauss. Initially, field strengths on smaller
scales will be larger, but nowhere near current levels.
| 1992-10-30
| 2007-05-23
|
[
"astro-ph"
] |
Ethan T. Vishniac
|
astro-ph/9210004
|
Dynamics of the Young Binary LMC Cluster NGC 1850
|
In this paper we have examined the age and internal dynamics of the young
binary LMC cluster NGC 1850 using BV CCD images and echelle spectra of 52
supergiants. Isochrone fits to a BV color-magnitude diagram revealed that the
primary cluster has an age of $\tau = 90 \pm 30$ Myr while the secondary member
has $\tau = 6 \pm 5$ Myr. BV surface brightness profiles were constructed out
to R $>$ 40 pc, and single-component King-Michie (KM) models were applied. The
total cluster luminosity varied from L$_B$ = 2.60 - 2.65 $\times 10^6$
L$_B$\sol\ and L$_V$ = 1.25 - 1.35 $\times 10^6$ as the anisotropy radius
varied from infinity to three times the scale radius with the isotropic models
providing the best agreement with the data. Of the 52 stars with echelle
spectra, a subset of 36 were used to study the cluster dynamics. The KM radial
velocity distributions were fitted to these velocities yielding total cluster
masses of 5.4 - 5.9 $\pm 2.4 \times 10^4$ M\sol\ corresponding to M/L$_B$ =
0.02 $\pm 0.01$ M\sol/L$_B$\sol\ or M/L$_V$ = 0.05 $\pm 0.02$ M\sol/L$_V$\sol.
A rotational signal in the radial velocities has been detected at the 93\%
confidence level implying a rotation axis at a position angle of 100\deg. A
variety of rotating models were fit to the velocity data assuming cluster
ellipticities of $\epsilon = 0.1 - 0.3$. These models provided slightly better
agreement with the radial velocity data than the KM models and had masses that
were systematically lower by a few percent. The preferred value for the slope
of a power-law IMF is a relatively shallow, $x = 0.29 \pmm{+0.3}{-0.8}$
assuming the B-band M/L or $x = 0.71 \pmm{+0.2}{-0.4}$ for the V-band.
| 1992-10-20
| 2009-10-22
|
[
"astro-ph"
] |
P. Fischer, D. L. Welch, and M. Mateo
|
astro-ph/9210005
|
Evidence for a Very Broad Line Region in PG 1138+222
|
We present a high S/N spectrum for the quasar PG 1138+222. We detect a very
broad HeII$\lambda$4686 emission line component with twice the FWHM of the
conventional broad line region (BLR) as evidenced by the Balmer lines. The
profile shape and centroid redshift also distinguish this HeII component from
the BLR features. The large ratio of HeII\l 4686 to any analogous H$\beta$
emission component is an indicator that it arises in a very high density region
($n_e \simgt 10^{11}-10^{13}$ \cm3). This Helium component is probably emitted
in a Very Broad Line Region (VBLR), where the radiation field is so strong that
the Str\"omgren depth becomes similar to the geometrical thickness of the
emitting clouds. The gas could therefore be optically thin to the Lyman
continuum.
| 1992-10-20
| 2009-10-22
|
[
"astro-ph"
] |
Paolo Marziani and Jack W. Sulentic
|
astro-ph/9210003
|
Cosmic Rays, Gamma Rays and Neutrinos from Point Sources
|
The suggestion has been made that the energy spectrum from point sources such
as AGN (Active Galactic Nuclei) and GBHC (Galactic Black Hole Candidates) is
universal, irrespective of the nature of the emitted particles. A comparison of
the energy spectrum for cosmic rays at the source and $\gamma$-rays from
quasars obtained recently by CGRO (Compton Gamma Ray Observatory) indicates
that the prediction is in agreement with the data in the average sense. This
suggests that neutrinos from point sources should have a spectral index
identical to that of $\gamma$-rays for an individual point source. This
prediction is also consistent with the recent observation of neutrinos by
Kamiokande and IMB in which the ratio of $\nu_\mu/\nu_e$ is close to 1, instead
of 2 as expected from atmospheric neutrinos. For a further test of the model,
analysis of the time variation of $\gamma$-ray spectra from quasars is
suggested.
| 1992-10-19
| 2009-10-22
|
[
"astro-ph"
] |
Yukio Tomozawa
|
astro-ph/9210002
|
Coordinated UV-optical observations of quasars: the evolution of the
Lyman absorption
|
The average flux decrement shortward the Ly$_{\alpha}$ emission, due to the
well-known ``forest'' of absorptions, has been measured in the spectra of 8
quasars. Quasi-simultaneous optical and IUE observations of the two low
redshift quasars PKS 0637--75 (z=0.654) and MC 1104+16 (z=0.632) have been
carried out, obtaining relatively high S/N, spectrophotometrically calibrated
data on their energy distribution from the rest frame H$_{\beta}$ to the Lyman
continuum. Six more quasars in the redshift range 2.5-3.4 have been observed in
the optical domain. For all the quasars the ``intrinsic'' continuum slope and
normalization have been estimated longward the Ly$_{\alpha}$ emission and
extrapolated towards the Lyman continuum to measure the average depressions,
which have been compared with the model statistics of the Ly$_{\alpha}$ clouds.
When all the known classes of absorbers are taken into account with plausible
values for their equivalent width distribution and evolution, a good agreement
is obtained with the observations. The results for the observed continuum
decrement at $z \sim 0.65$ are identical to those predicted by the evolution
with redshift of the number of Ly$_{\alpha}$ forest systems including the HST
data and within $2\sigma$ of the predicted value using the ``standard''
Ly$_{\alpha}$ evolution (as determined only at high z).
| 1992-10-14
| 2007-05-23
|
[
"astro-ph"
] |
S. Cristiani, E. Giallongo, L. M. Buson, C. Gouiffes, F. La Franca
|
astro-ph/9210001
|
The Edge of the Galactic Disc
|
As part of a stellar population sampling program, a series of photometric
probes at various field sizes and depths have been obtained in a low extinction
window in the galactic anticentre direction. Such data set strong constraints
on the radial structure of the disc. At the forefront of this "drilling"
program, very deep CCD frames probe the most external parts of the disc. Over
the whole effective magnitude range (18 to 25), all contributions in the
statistics which should be expected from old disc stars beyond 6 kpc vanish,
although such stars dominate by far at distances less than 5 kpc. This is the
signature of a sharp cut-off in the star density: the edge of the galactic disc
between 5.5 and 6 kpc. As a consequence, the galactic radius does not exceed 14
kpc (assuming $R/-/(//sun/)$=8.5). Colours of elliptical galaxies measured in
the field rule out the risk of being misled by undetected extinction.
| 1992-10-02
| 2009-10-22
|
[
"astro-ph"
] |
Annie C. Robin, Michel Creze, Vijay Mohan
|
astro-ph/9209006
|
Inflation at the Electroweak Scale
|
We present a simple model for slow-rollover inflation where the vacuum energy
that drives inflation is of the order of $G_F^{-2}$; unlike most models, the
conversion of vacuum energy to radiation (``reheating'') is moderately
efficient. The scalar field responsible for inflation is a standard-model
singlet, develops a vacuum expectation value of the order of $4\times
10^6\GeV$, has a mass of order $1\GeV$, and can play a role in electroweak
phenomena.
| 1992-09-30
| 2009-10-22
|
[
"astro-ph",
"hep-ph"
] |
L. Knox and M.S. Turner (U. of Chicago/Fermilab)
|
astro-ph/9209005
|
Neutrino Flavor Conversion in a Supernova Core
|
If $\nu_\mu$ or $\nu_\tau$ mix with $\nu_e$, neutrino oscillations and
collisions in a supernova (SN) core allow these flavors effectively to
participate in $\beta$ equilibrium and thus to obtain a large chemical
potential. If a sterile species mixes with $\nu_e$, these effects lead to an
anomalous loss of energy and lepton number. We study flavor conversion in a SN
core on the basis of a new kinetic equation which rigorously includes neutrino
interference and degeneneracy effects. Our discussion serves as an example and
illustration of the properties of this ``non-abelian Boltzmann equation''.
| 1992-09-24
| 2009-10-22
|
[
"astro-ph",
"hep-ph"
] |
G. Raffelt and G. Sigl
|
astro-ph/9209004
|
On the Tail Problem in Cosmology
|
The tail problem for the propagation of a scalar field is considered in a
cosmological background, taking a Robertson-Walker spacetime as a specific
example. The explicit radial dependence of the general solution of the
Klein-Gordon equation with nonminimal coupling is derived, and the
inapplicability of the standard calculation of the reflection and transmission
coefficients to the study of scattering of waves by the cosmological curvature
is discussed.
| 1992-09-23
| 2009-10-22
|
[
"astro-ph"
] |
Valerio Faraoni and Sebastiano Sonego
|
astro-ph/9209003
|
The Spectral Index in the CDM Cosmogony
|
In a recent paper, we suggested that the density fluctuation spectra arising
from power-law (or extended) inflation, which are tilted with respect to the
Harrison--Zel'dovich spectrum, may provide an explanation for the excess large
scale clustering seen in galaxy surveys such as the APM survey. In the light of
the new results from COBE, we examine in detail here cold dark matter
cosmogonies based on inflationary models predicting power-law spectra. Along
with power-law and extended inflation, this class includes natural inflation.
The latter is of interest because, unlike the first two, it produces a
power-law spectrum without significant gravitational wave production. We
examine a range of phenomena, including large angle microwave background
fluctuations, clustering in the galaxy distribution, bulk peculiar velocity
flows, the formation of high redshift quasars and the epoch of structure
formation. Of the three models, only natural inflation seems capable of
explaining the large scale clustering of optical galaxies. Such a model, though
at best marginal even at present, has some advantages over standard CDM and on
most grounds appears to perform at least as well. Power-law inflation's primary
interest may ultimately only be in permitting a larger bias parameter than
standard CDM; it appears unable to explain excess clustering. Most models of
extended inflation are ruled out at a high confidence level.
| 1992-09-13
| 2007-05-23
|
[
"astro-ph",
"gr-qc",
"hep-ph"
] |
David H Lyth and Andrew A Liddle
|
astro-ph/9209002
|
Extended Hot Gas Halos Around Starburst Galaxies
|
Reanalysis of Einstein IPC data and new observations from the GINGA
LAC indicate the presence of extended X-ray emission (10-50 kpc) around the
starburst galaxy M82. Here we model this emission by calculating numerical
hydrodynamic simulations of the starburst event to much later times and larger
scales than previously considered. For our models, we adopt a supernova rate of
0.1 ${\rm yr}^{-1}$, and an extended low-density static halo that is bound to
the galaxy. There are three stages to the evolution of the wind-blown bubble
and the propagation of the shock front: the bubble expands in an almost uniform
density disk gas, with a deceleration of the shock front ($t \alt $ 3.6 Myr);
breakout from the disk and the upward acceleration of the shock front (3.6
Myr $\alt t \alt$ 18 Myr); propagation into the halo, leading to a more
spherical system and shock deceleration (18 Myr $\alt t$). For a halo density
of $10^{-3} {\rm cm}^{-3}$, the outflow reaches a distance of 40-50 kpc from
the center of the starburst galaxy in 50 Myr. We calculate the time evolution
of the X-ray luminosity and find that the extended starburst emits $3\times
10^{39}\lcgs$ to $10^{40}\lcgs$ in the
GINGA LAC band and $\sim 10^{41}\lcgs$ in the Einstein or ROSAT
HRI band. The degree of the ionization equilibrium in the outflow and its
effect on the iron K$\alpha$ line emission are discussed.
| 1992-09-12
| 2007-05-23
|
[
"astro-ph"
] |
Kohji Tomisaka and Joel N. Bregman
|
astro-ph/9209001
|
The Radial Structure of the Galactic Disc
|
Three colour photometry on CCD frames in the Special Area SpA23 provides a
deep probe of the galactic disc in a low absorption window towards the
anticenter. Magnitudes to better than 10% at V = 25 and B-V colour down to V =
23 have been obtained. These new data, used in combination with lower magnitude
photographic data in a wider field, give a strong evidence that the galactic
density scale length is rather short (2.5 kpc) and drops abruptly beyond 6 kpc.
| 1992-09-04
| 2011-05-23
|
[
"astro-ph"
] |
Annie C. Robin, Michel Creze, Vijay Mohan
|
astro-ph/9208006
|
Binary Black Holes in Stationary Orbits
|
We show that under certain astrophysical conditions a binary system
consisting of two compact objects can be stabilized against indefinite
shrinking of orbits due to the emission of gravitational radiation. In this
case, the lighter binary companion settles down to a stable orbit when the loss
of the angular momentum due to gravitational radiation becomes equal to its
gain from the accreting matter from the disk around the more massive primary.
We claim that such systems can be stable against small perturbations and can be
regarded as steady emitters of gravitational waves of constant frequency and
amplitude. Furthermore, X-rays emitted by the secondary can also produce
astrophysically interesting situations when coupled with gravitational lensing
and Doppler effects.
| 1992-08-27
| 2007-05-23
|
[
"astro-ph",
"gr-qc"
] |
Sandip K. Chakrabarti (Tata Institute of Fundamental Research, Bombay,
INDIA)
|
astro-ph/9208007
|
COBE, Gravitational Waves, Inflation and Extended Inflation
|
We analyse the implications for inflationary models of the cosmic microwave
background (cmb) anisotropy measured by COBE. Vacuum fluctuations during
inflation generate an adiabatic density perturbation, and also gravitational
waves. The ratio of these two contributions to the cmb anisotropy is given for
an arbitrary slow-roll inflaton potential. Results from the IRAS/QDOT and
POTENT galaxy surveys are used to normalise the spectrum of the density
perturbation on the scale $20h^{-1}\Mpc$, so that the COBE measurement on the
scale $10^3h^{-1}\Mpc$ provides a lower bound on the spectral index $n$. For
`power law' and `extended' inflation, gravitational waves are significant and
the bound is $n>0.84$ at the $2$-sigma level. For `natural' inflation,
gravitational waves are negligible and the constraint is weakened to $n>0.70$,
at best marginally consistent with a recent proposal for explaining the excess
clustering observed in the APM galaxy survey. Many versions of extended
inflation, including those based on the Brans--Dicke theory, are ruled out,
because they require $n\lsim 0.75$ in order that bubbles formed at the end of
inflation should not be observed now in the cmb.
| 1992-08-27
| 2009-10-22
|
[
"astro-ph",
"gr-qc",
"hep-ph"
] |
David H Lyth and Andrew R Liddle
|
astro-ph/9208005
|
The Last Three Minutes: Issues in Gravitational Wave Measurements of
Coalescing Compact Binaries
|
Gravitational-wave interferometers are expected to monitor the last three
minutes of inspiral and final coalescence of neutron star and black hole
binaries at distances approaching cosmological, where the event rate may be
many per year. Because the binary's accumulated orbital phase can be measured
to a fractional accuracy $\ll 10^{-3}$ and relativistic effects are large, the
waveforms will be far more complex, carry more information, and be far harder
to model theoretically than has been expected. Theorists must begin now to lay
a foundation for extracting the waves' information.
| 1992-08-25
| 2009-07-09
|
[
"astro-ph",
"gr-qc"
] |
Curt Cutler, Theocharis A. Apostolatos, Lars Bildsten, Lee Samuel
Finn, Eanna E. Flanagan, Daniel Kennefick, Dragoljubov M. Markovic, Amos Ori,
Eric Poisson, Gerald Jay Sussman, and Kip S. Thorne
|
astro-ph/9208004
|
Constraints on radiative decay of the 17-keV neutrino from COBE
Measurements
|
It is shown that, for a nontrivial radiative decay channel of the 17-keV
neutrino, the photons would distort the microwave background radiation through
ionization of the universe. The constraint on the branching ratio of such
decays from COBE measurements is found to be more stringent than that from
other considerations. The limit on the branching ratio in terms of the Compton
$y$ parameter is $B_\gamma < 1.5 \times 10^{-7} ({\tau_\nu \over 10^{11}
sec})^{0.45} ({y \over 10^{-3}})^{1.11} h^{-1}$ for an $\Omega=1, \Omega_b=0.1$
universe.
| 1992-08-12
| 2009-10-22
|
[
"astro-ph",
"hep-ph"
] |
Biman B. Nath
|
astro-ph/9208003
|
The Probability for Formation of Collapsing Textures and Texture Knots
|
Global textures are interesting because they are promising candidates for
seeds in the structure formation of the universe. The important configurations
are those who will be able to collapse. The type of configurations that I will
consider are half knots and true knots. I define a half knot as one that covers
more than a half-$S^3$, and a true knot as a configuration that covers the
whole of $S^3$. Configurations that are half knots will be able to collapse, a
new argument for this collapse criterion is given in this paper. I also give
some critical remarks on the method of using the total winding number as a
criterion for identifying a knot. I propose another more direct method and make
use of it when I estimate the probability for formation of both true and half
knots by numerical simulations.Taking into account the chance of annihilation
the probability for collapse is found to be in the interval $p_{coll} \in
[0.01,0.04]$. In the skyrmion picture of hadrons the investigations of
formation of true knots are important, and some implications of my result on
the predictions of a "topological" theory of baryon production in jets are
discussed.
| 1992-08-07
| 2011-07-19
|
[
"astro-ph",
"hep-th"
] |
Stefan {\AA}minneborg (Stockholm University)
|
astro-ph/9208002
|
Dependence of Density Perturbations on the Coupling Constant in a Simple
Model of Inflation
|
In the standard inflationary scenario with inflaton potential
$V(\Phi)=M^4-{1\over4}\lambda\Phi^4$, the resulting density perturbations
$\delta\rho/\rho$ are proportional to $\lambda^{1/2}$. Upper bounds on
$\delta\rho/\rho$ require $\lambda < 10^{-13}$. Ratra has shown that an
alternative treatment of reheating results in $\delta\rho/\rho \propto
\lambda^{-1}$, so that an upper bound on $\delta\rho/\rho$ does not put an
obvious upper bound on $\lambda$. We verify that $\delta\rho/\rho \propto
\lambda^{-1}$ is indeed a possibility, but show that $\lambda < 10^{-13}$ is
still required.
| 1992-08-04
| 2009-10-22
|
[
"astro-ph"
] |
Toby Falk, Raghavan Rangarajan, and Mark Srednicki
|
astro-ph/9208001
|
The Angular Dependence of the Three-Point Correlation Function of the
Cosmic Microwave Background Radiation as Predicted by Inflationary
Cosmologies
|
Inflationary models predict a definite, model independent, angular dependence
for the three-point correlation function of $\Delta T/T$ at large angles
(greater than $\sim 1^\circ$) which we calculate. The overall amplitude is
model dependent and generically unobservably small, but may be large in some
specific models. We compare our results with other models of nongaussian
fluctuations.
| 1992-08-04
| 2009-10-22
|
[
"astro-ph",
"hep-ph"
] |
Toby Falk, Raghavan Rangarajan, and Mark Srednicki
|
astro-ph/9207001
|
Cosmic Microwave Background Probes Models of Inflation
|
Inflation creates both scalar (density) and tensor (gravity wave) metric
perturbations. We find that the tensor mode contribution to the CMB anisotropy
on large-angular scales can only exceed that of the scalar mode in models where
the spectrum of perturbations deviates significantly from scale invariance
(e.g., extended and power-law inflation models and extreme versions of chaotic
inflation). If the tensor mode dominates at large-angular scales, then the
value of $\Delta T/T$ predicted on $1^\circ$ is less than if the scalar mode
dominates, and, for cold dark matter models, $b>1$ can be made consistent with
the COBE DMR results.
| 1992-07-13
| 2009-09-15
|
[
"astro-ph",
"hep-ph"
] |
R.L. Davis, H.M. Hodges, G.F. Smoot, P.J. Steinhardt, M.S. Turner
|
astro-ph/9207002
|
Graceful Exit in Extended Inflation and Implications for Density
Perturbations
|
Two qualitatively different modes of ending superluminal expansion are
possible in extended inflation. One mode, different from the one envoked in
most extended models to date, easily avoids making big bubbles that distort the
cosmic microwave background radiation (CMBR). In this mode, the spectrum of
density fluctuations is found to be scale-free, $P(k) \propto k^n$, where $n$
might lie anywhere between 0.5 and 1.0 (whereas, previously, it appeared that
the range $1.0> n \gtsim 0.84$ was disallowed).
| 1992-07-13
| 2009-09-15
|
[
"astro-ph",
"hep-ph"
] |
R. Crittenden and Paul J. Steinhardt
|
astro-ph/9206005
|
Entropy of a Classical Stochastic Field and Cosmological Perturbation
|
We propose a general definition of nonequilibrium entropy of a classical
stochastic field. As an example of particular interest in cosmology we apply
this definition to compute the entropy of density perturbations in an
inflationary Universe. On the scales of structures in the Universe, the entropy
of density perturbations dominates over the statistical fluctuations of the
entropy of cosmic microwave photons, indicating the relevance of the entropy of
density fluctuations for structure formation.
| 1992-06-24
| 2009-10-22
|
[
"astro-ph",
"hep-ph"
] |
R. Brandenberger (Brown), V. Mukhanov (ETH Zuerich) and T. Prokopec
(Brown)
|
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