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alg-geom/9511001
GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau Hypersurfaces
We present a detailed study of the generalized hypergeometric system introduced by Gel'fand, Kapranov and Zelevinski (GKZ-hypergeometric system) in the context of toric geometry. GKZ systems arise naturally in the moduli theory of Calabi-Yau toric varieties, and play an important role in applications of the mirror symm...
1995-11-01
2009-10-28
[ "alg-geom", "hep-th", "math.AG" ]
S.Hosono, B.H.Lian and S.-T.Yau
alg-geom/9510018
Mixed Hodge structures of configuration spaces
The symmetric group S_n acts freely on the configuration space of n distinct points in a quasi-projective variety. In this paper, we study the induced action of the symmetric group S_n on the de Rham cohomology of this space, using mixed Hodge theory, combined with methods from the theory of symmetric functions. (We pr...
1995-11-01
2008-02-03
[ "alg-geom", "math.AG" ]
Ezra Getzler
alg-geom/9510017
Explicit Enumerative Geometry for the Real Grassmannian of Lines in Projective Space
We extend the classical Schubert calculus of enumerative geometry for the Grassmann variety of lines in projective space from the complex realm to the real. Specifically, given any collection of Schubert conditions on lines in projective space which generically determine a finite number of lines, we show there exist re...
1995-10-31
2008-02-03
[ "alg-geom", "math.AG" ]
Frank Sottile
alg-geom/9510016
Infinite Grassmannians and Moduli Spaces of G-bundles
This lecture note is devoted to prove that the space of vacua is isomorphic with the space of generalized theta functions (joint work with M.S. Narasimhan, and A. Ramanathan)
1995-10-30
2008-02-03
[ "alg-geom", "math.AG" ]
Shrawan Kumar
alg-geom/9510015
Rational curves of degree at most 9 on a general quintic threefold
We prove the following form of the Clemens conjecture in low degree. Let $d\le9$, and let $F$ be a general quintic threefold in $\IP^4$. Then (1)~the Hilbert scheme of rational, smooth and irreducible curves of degree $d$ on $F$ is finite, nonempty, and reduced; moreover, each curve is embedded in $F$ with normal bundl...
1995-10-30
2008-02-03
[ "alg-geom", "math.AG" ]
Trygve Johnsen and Steven L. Kleiman
alg-geom/9510014
Manin's conjecture for toric varieties
We prove an asymptotic formula conjectured by Manin for the number of $K$-rational points of bounded height with respect to the anticanonical line bundle for arbitrary smooth projective toric varieties over a number field $K$.
1995-10-26
2008-02-03
[ "alg-geom", "math.AG" ]
Victor V. Batyrev and Yuri Tschinkel
alg-geom/9510013
Second N=1 Superanalog of Complex Structure
We found another N=1 odd superanalog of complex structure (the even one is widely used in the theory of super Riemann surfaces). New N=1 superconformal-like transformations are similar to anti-holomorphic ones of nonsupersymmetric complex function theory. They are dual to the ordinary superconformal transformations sub...
1995-10-19
2009-10-28
[ "alg-geom", "hep-th", "math.AG" ]
Steven Duplij
alg-geom/9510012
Lectures on Seiberg-Witten Invariants
These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.
1995-10-15
2008-02-03
[ "alg-geom", "math.AG" ]
Selman Akbulut (Michigan State University)
alg-geom/9510011
Parabolic Higgs bundles and Teichm\"uller spaces for punctured surfaces
In this paper we study the relation between parabolic Higgs bundles and irreducible representations of the fundamental group of punctured Riemann surfaces established by Simpson. We generalize a result of Hitchin, identifying those parabolic Higgs bundles that correspond to Fuchsian representations. We also study the H...
1995-10-14
2007-07-31
[ "alg-geom", "hep-th", "math.AG" ]
Indranil Biswas, Pablo Gastesi and Suresh Govindarajan
alg-geom/9510010
Quantum cohomology of projective bundles over $\Pee^n$
Results in the preliminary version have been strengthed. In addition, Batyrev's conjectural formula for quantum cohomology of projective bundles associated to direct sum of line bundles over $\Pee^n$ is partially verified.
1995-10-14
2008-02-03
[ "alg-geom", "math.AG" ]
Zhenbo Qin and Yongbin Ruan
alg-geom/9510009
Nilpotent groups and universal coverings of smooth projective varieties
In this paper we prove that the universal cover of a smooth projective variety with nilpotent fundamental group is holomorphically convex.
1995-10-13
2008-02-03
[ "alg-geom", "math.AG" ]
Ludmil Katzarkov
alg-geom/9510008
K3 surfaces, Lorentzian Kac--Moody algebras and Mirror Symmetry
We consider the variant of Mirror Symmetry Conjecture for K3 surfaces which relates "geometry" of curves of a general member of a family of K3 with "algebraic functions" on the moduli of the mirror family. Lorentzian Kac--Moody algebras are involved in this construction. We give several examples when this conjecture is...
1995-10-08
2008-02-03
[ "alg-geom", "hep-th", "math.AG", "math.QA", "q-alg" ]
Valeri A. Gritsenko and Viacheslav V. Nikulin
alg-geom/9510006
Some Remarks on Beilinson Adeles
This paper contains two remarks on Beilinson's adeles with values in the De Rham complex of a scheme. The first is an interpretation, in terms of adeles, of the decomposition of the De Rham complex on a scheme defined modulo $p^{2}$ (the result of Deligne-Illusie). The second remark is about the possible relation betwe...
1995-10-05
2008-02-03
[ "alg-geom", "math.AG" ]
Amnon Yekutieli
alg-geom/9510005
On the Brill-Noether Problem for Vector Bundles
On an arbitrary compact Riemann surface, necessary and sufficient conditions are found for the existence of semistable vector bundles with slope between zero and one and a prescribed number of linearly independent holomorphic sections. Existence is achieved by minimizing the Yang-Mills-Higgs functional.
1995-10-05
2008-02-03
[ "alg-geom", "math.AG" ]
Georgios Daskalopoulos, and Richard Wentworth
alg-geom/9510007
Smooth Formal Embeddings and the Residue Complex
Let \pi : X -> S be a finite type morphism of noetherian schemes. A smooth formal embedding of X (over S) is a bijective closed immersion X -> \frak{X}, where \frak{X} is a noetherian formal scheme, formally smooth over S. An example of such an embedding is the formal completion \frak{X} = Y_{/X} where X \subset Y is a...
1995-10-05
2008-02-03
[ "alg-geom", "math.AG" ]
Amnon Yekutieli
alg-geom/9510004
On Fujita's freeness conjecture for 3-folds and 4-folds
The result on 3-fold is now optimal by the result of Ein-Lazarsfeld and Helmke.
1995-10-03
2008-02-03
[ "alg-geom", "math.AG" ]
Yujiro Kawamata
alg-geom/9510001
The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface
We prove that the weight-two Hodge structure of moduli spaces of torsion-free sheaves on a K3 surface is as described by Mukai (the rank is arbitrary but we assume the first Chern class is primitive). We prove the moduli space is an irreducible symplectic variety (by Mukai's work it was known to be symplectic). By work...
1995-10-02
2008-02-03
[ "alg-geom", "math.AG" ]
Kieran G. O'Grady
alg-geom/9510002
Finiteness Theorem for Sp(4,Z)
We consider Siegel upper half space of rank two ${\cal H}^2$ and different subgroups $H\subseteq {\bf Sp(4,Z)}$ of finite index. The purpose of this paper is to prove that the field of rational functions of ${\cal H}^2/H$ has general type for all but the finite number of $H$.
1995-10-02
2008-02-03
[ "alg-geom", "math.AG" ]
Lev A. Borisov
alg-geom/9509009
Mirror duality and string-theoretic Hodge numbers
We prove in full generality the mirror duality conjecture for string-theoretic Hodge numbers of Calabi-Yau complete intersections in Gorenstein toric Fano varieties. The proof is based on properties of intersection cohomology
1995-10-01
2009-10-28
[ "alg-geom", "hep-th", "math.AG" ]
Victor V. Batyrev and Lev A. Borisov
alg-geom/9509008
Bogomolov conjecture for curves of genus 2 over function fields
In this note, we will show that Bogomolov conjecture holds for a non-isotrivial curve of genus 2 over a function field.
1995-10-01
2008-02-03
[ "alg-geom", "math.AG" ]
Atsushi Moriwaki
alg-geom/9509007
Obstruction bundles, semiregularity, and Seiberg-Witten invariants
We compare the deformation theory and the analytic structure of the Seiberg-Witten moduli spaces of a K\"ahler surface to the corresponding components of the Hilbert scheme, and show that they are isomorphic. Next we show how to compute the invariant in case the moduli space is smooth but not of the expected dimension,...
1995-09-29
2008-02-03
[ "alg-geom", "math.AG" ]
Robert Friedman, John W. Morgan
alg-geom/9509006
The Toda hierarchy and the KdV hierarchy
The Toda hierarchy of size $N$ is well known to be analogous to the KdV hierarchy at $N$ goes to infinity. This paper shows that given $f$ a periodic function, there is a canonical way of defining the initial data for the Toda lattice equations so that the evolution of this data under the Toda lattice hierarchy looks a...
1995-09-26
2009-10-28
[ "alg-geom", "math.AG" ]
D. Gieseker
alg-geom/9509005
Gorenstein algebras, symmetric matrices, self-linked ideals, and symbolic powers
Inspired by recent work in the theory of central projections onto hypersurfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert--Burch matrix that has a maximal symmetric subblock. We also prove that every Gorenstein perfect algebra of grade 1 can be presented, as a module, by a symmetric...
1995-09-10
2008-02-03
[ "alg-geom", "math.AC", "math.AG" ]
Steven Kleiman, and Bernd Ulrich
alg-geom/9509004
The Canonical Class of $\overline{M}_{0,n}(P^r,d)$ And Enumerative Geometry
D. Abramovich found an error in the singularity analysis in the first posting of this paper affecting one formula (Thanks Dan).The error has been corrected. Only the arithmetic genus formula has changed. The geometric genus and all the canonical class formulas are the same.
1995-09-03
2008-02-03
[ "alg-geom", "math.AG" ]
R. Pandharipande
alg-geom/9509003
Generators for Symbolic Powers of Ideals Defining General Points of $P^2$
Given distinct points $p_1,\cdots,p_r$ of the projective plane $P^2$ and a positive integer $m$, the homogeneous ideal defining the fat point subscheme $Z=m(p_1+\cdots+p_r)$ is the symbolic power $I^{(m)}$ of the homogeneous ideal $I$ defining the smooth union of the $r$ points $p_1,\ldots,p_r$. If $p_1,\ldots,p_r$ are...
1995-09-01
2011-11-09
[ "alg-geom", "math.AG" ]
Brian Harbourne
alg-geom/9509002
Free Resolutions of Fat Point Ideals on $P^2$
By defining a fat point subscheme of $P^2$ to be a 0-dimensional subscheme defined by a sheaf of integrally closed ideals one extends the notion of fat point subschemes to allow infinitely near points. With this notion of fat points, this preprint determines the number of generators in each degree in a minimal homogene...
1995-09-01
2009-09-25
[ "alg-geom", "math.AG" ]
Brian Harbourne
alg-geom/9509001
Anticanonical Rational Surfaces
A determination of the fixed components, base points and irregularity is made for arbitrary numerically effective divisors on any smooth projective rational surface having an effective anticanonical divisor. All of the results are proven over an algebraically closed field of arbitrary characteristic. Applications, trea...
1995-09-01
2009-09-25
[ "alg-geom", "math.AG" ]
Brian Harbourne
alg-geom/9508012
Quotients by Groupoids
We show that if a flat group scheme acts properly, with finite stabilizers, on an algebraic space, then a quotient exists as a separated algebraic space. More generally we show any flat groupid for which the family of stabilizers is finite has a uniform geometric, uniform categorical quotient in the category of algebra...
1995-08-25
2008-02-03
[ "alg-geom", "math.AG" ]
Sean Keel, Shigefumi Mori
alg-geom/9508011
On the quantum cohomology of the plane, old and new
We describe a method for counting maps of curves of given genus (and variable moduli) to $\Bbb P^2$, essentially by splitting the $\Bbb P^2$ in two; then specialising to the case of genus 0 we show that the method of quantum cohomology may be viewed as the 'mirror' of the former method where one splits the $\Bbb P^1$ r...
1995-08-23
2008-02-03
[ "alg-geom", "math.AG" ]
Ziv Ran
alg-geom/9508010
Actions of groups of birationally extendible automorphisms
We study the actions of a Lie group $G$ by birationally extendible automorphisms on a domain $D\subset C^n$. For a large class of such domains defined by polynomial inequalities, all automorphisms are of this type. In the cases 1) $G$ has finitely many components or 2) the degree of the automorphisms is bounded, we pro...
1995-08-22
2008-02-03
[ "alg-geom", "math.AG", "math.CV" ]
Alan Huckleberry, Dmitri Zaitsev
alg-geom/9508008
Zagier's conjecture on $L(E,2)$
In this paper we introduce an elliptic analog of the Bloch-Suslin complex and prove that it (essentially) computes the weight two parts of the groups $K_2(E)$ and $K_1(E)$ for an elliptic curve $E$ over an arbitrary field $k$. Combining this with the results of Bloch and Beilinson we proved Zagier's conjecture on $L(E,...
1995-08-17
2008-02-03
[ "alg-geom", "math.AG" ]
A.B. Goncharov, A.M. Levin
alg-geom/9508009
Frobenius morphisms over Z/p^2 and Bott vanishing
Let $X$ be a smooth projective algebraic variety over $Z/p$, which has a flat lift to a scheme $X'$ over $Z/p^2$. If the absolute Frobenius morphism $F$ on $X$ lifts to a morphism on $X'$, then an old trick by Mazur shows that push-down of the de Rham complex under $F$ decomposes. We show that the quasi-isomorphism in ...
1995-08-17
2008-02-03
[ "alg-geom", "math.AG" ]
A. Buch, J. F. Thomsen, N. Lauritzen and V. B. Mehta
alg-geom/9508007
Geometry of plane curves via Tschirnhausen resolution tower
We show the existence of toric resolution tower for an irreducible curve singularity which is explicitly described by Tschirnhausen polynomials. We deduce for a smooth affine plane curve from its topology restrictions for its singularity at infinity. For instance, we discribe the singularities at infinity (up to equisi...
1995-08-16
2015-06-30
[ "alg-geom", "math.AG" ]
Norbert A'Campo and Mutsuo Oka
alg-geom/9508006
Topological Classifying Spaces of Lie Algebras and the Natural Completion of Contractions
The space K^n of all n-dimensional { Lie} algebras has a natural non-Hausdorff topology k^n, which has characteristic limits, called transitions, A -> B, between distinct Lie algebras A and B. The entity of these transitions are the natural transitive completion of the well known Inonu-Wigner contractions and their par...
1995-08-15
2008-02-03
[ "alg-geom", "math.AG", "math.QA", "q-alg" ]
M. Rainer
alg-geom/9508005
Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
This article contains an elementary constructive proof of resolution of singularities in characteristic zero. Our proof applies in particular to schemes of finite type and to analytic spaces (so we recover the great theorems of Hironaka). We introduce a discrete local invariant $\inv_X (a)$ whose maximum locus determin...
1995-08-15
2008-02-03
[ "alg-geom", "math.AG" ]
Edward Bierstone, and Pierre Milman
alg-geom/9508004
Grothendieck topologies and deformation theory II
This paper is a continuation of ``Operads, Grothendieck topologies and deformation theory'' (alg-geom/9502010). We show how to develop a cohomology theory that would control deformations of a sheaf of associative algebras over a scheme by means of introducing an appropriate site and considering sheaves on it.
1995-08-08
2008-02-03
[ "alg-geom", "math.AG" ]
Dennis Gaitsgory
alg-geom/9508003
Heights for line bundles on arithmetic surfaces
For line bundles on arithmetic varieties we construct height functions using arithmetic intersection theory. In the case of an arithmetic surface, generically of genus g, for line bundles of degree g equivalence is shown to the height on the Jacobian defined by the Theta divisor.
1995-08-06
2008-02-03
[ "alg-geom", "math.AG" ]
Joerg Jahnel
alg-geom/9508002
Modular subvarieties of arithmetic quotients of bounded symmetric domains
Arithmetic quotients are quotients of bounded symmetric domains by arithmetic groups, and modular subvarieties of arithmetic quotients are themselves arithmetic quotients of lower dimension which live on arithmetic quotients, by an embedding induced from an inclusion of groups of hermitian type. We show the existence o...
1995-08-02
2008-02-03
[ "alg-geom", "math.AG" ]
Bruce Hunt
alg-geom/9508001
Localization in equivariant intersection theory and the Bott residue formula
The purpose of this paper is to prove the localization theorem for torus actions in equivariant intersection theory. Using the theorem we give another proof of the Bott residue formula for Chern numbers of bundles on smooth complete varieties. In addition, our techniques allow us to obtain residue formulas for bundles ...
1995-08-01
2008-02-03
[ "alg-geom", "math.AG" ]
Dan Edidin and William Graham
alg-geom/9507017
Spectral curves, algebraically completely integrable Hamiltonian systems, and moduli of bundles
This is the expanded text of a series of CIME lectures. We present an algebro-geometric approach to integrable systems, starting with those which can be described in terms of spectral curves. The prototype is Hitchin's system on the cotangent bundle of the moduli space of stable bundles on a curve. A variant involving ...
1995-07-31
2008-02-03
[ "alg-geom", "math.AG" ]
Ron Donagi and Eyal Markman
alg-geom/9507016
Degenaration of Calabi-Yau Manifold with W-P Metric
In this paper we focus on determining for which degenerations the central fibre is at finite distance with respect to Weil-Petersson metric. We obtain a simple condition on the limiting mixed Hodge structure. Then we combine the result with the canonical mixed Hodge structure of the central fibre and obtain a simple co...
1995-07-28
2008-02-03
[ "alg-geom", "math.AG" ]
Yoshiko Hayakawa
alg-geom/9507015
Correlation for Surfaces of General Type
The main geometric result of this paper is that given any family of surfaces of general type f:X-->B, for sufficiently large n the fiber product X^n_B dominates a variety of general type. This result is especially interesting when it is combined with Lang's Conjecture. This states that for a variety V of general type o...
1995-07-26
2008-02-03
[ "alg-geom", "math.AG" ]
Brendan Hassett
alg-geom/9507014
All strictly exceptional collections in $D^b_{coh}(P^m)$ consist of vector bundles
It is proved that any strictly exceptional collection generating the derived category of coherent sheaves on a smooth projective variety X with \rk K_0(X) = \dim X + 1 constists of locally free sheaves up to a common shift.
1995-07-26
2013-10-29
[ "alg-geom", "math.AG" ]
Leonid Positselski
alg-geom/9507013
Descent, Motives and K-theory
To an arbitrary variety over a field of characteristic zero, we associate a complex of Chow motives, which is, up to homotopy, unique and bounded. We deduce that any variety has a natural Euler characteristic in the Grothendieck group of Chow motives. We show that the cohomology with integer coefficients of any singula...
1995-07-21
2008-02-03
[ "alg-geom", "math.AG" ]
Henri Gillet and Christophe Soule
alg-geom/9507012
Heisenberg algebra and Hilbert schemes of points on projective surfaces
I have just replaced the first line by %&amslplain in order to be compiled by AMS-LaTeX.
1995-07-20
2008-02-03
[ "alg-geom", "math.AG" ]
Hiraku Nakajima
alg-geom/9507011
A Projective Surface of Degree Eight with 168 Nodes
The estimate for the maximal number of ordinary double points of a projective surface of degree eight is improved to $168\leq\mu(8)\leq 174$ by constructing a projective surface of degree eight with 168 nodes.
1995-07-19
2008-02-03
[ "alg-geom", "math.AG" ]
Stephan Endrass
alg-geom/9507010
Koszul duality and Galois cohomology
It it shown that the Bloch-Kato conjecture on the norm residue homomorphism $K^M(F)/l \to H^*(G_F,Z/l)$ follows from its (partially known) low-degree part under the assumption that the Milnor K-theory algebra $K^M(F)/l$ modulo $l$ is Koszul. This conclusion is a case of a general result on the cohomology of nilpotent (...
1995-07-11
2013-10-29
[ "alg-geom", "math.AG" ]
Leonid Positselski and Alexander Vishik
alg-geom/9507008
The Gauss map and the dual variety of real-analytic submanifolds in a sphere or in a hyperbolic space
We study the Gauss map and the dual variety of a real-analytic immersion of a connected compact real-analytic manifold into a sphere or into a hyperbolic space. The dual variety is defined to be the set of all normal directions of the immersion. First, we show that the image of the Gauss map characterizes the manifold....
1995-07-09
2010-06-21
[ "alg-geom", "dg-ga", "math.AG", "math.DG" ]
Tohsuke Urabe
alg-geom/9507009
Remarks on Seshadri constants
Given a smooth complex projective variety $X$ and an ample line bundle $L$ on $X$. Fix a point $x\in X$. We consider the question, are there conditions which guarantee the maxima of the Seshadri constant of $L$ at $x$, i.e $\eps(L,x)=\root n \of {L^n}$? We give a partial answer for surfaces and find examples where ...
1995-07-09
2008-02-03
[ "alg-geom", "math.AG" ]
Andreas Steffens
alg-geom/9507003
A note on scrolls of smallest embedded codimension
Let $M$ be a submanifold of ${\Bbb P}^N$ of dimension $n>2$. Suppose that $(M,{\Cal O}_M(1))\cong{\Bbb P}({\Cal E}),{\Cal O}(1))$ for some vector bundle ${\Cal E}$ on a surface $S$. Then $N\ge 2n-1$ by Barth-Lefschetz Theorem. We are interested in the case $N=2n-1$. In 1994 Ionescu and Toma gave a classification of the...
1995-07-07
2008-02-03
[ "alg-geom", "math.AG" ]
Takao Fujita
alg-geom/9507006
A Noether-Lefschetz theorem for vector bundles
In this note we use the monodromy argument to prove a Noether-Lefschetz theorem for vector bundles.
1995-07-07
2008-02-03
[ "alg-geom", "math.AG" ]
Jeroen G. Spandaw
alg-geom/9507005
On the number of singular points of plane curves
This is an extended, renovated and updated report on a joint work which the second named author presented at the Conference on Algebraic Geometry held at Saitama University, 15-17 of March, 1995. The main result is an inequality for the numerical type of singularities of a plane curve, which involves the degree of the ...
1995-07-07
2008-02-03
[ "alg-geom", "math.AG" ]
S. Orevkov and M. Zaidenberg
alg-geom/9507007
On the diffeomorphism groups of elliptic surfaces
In this paper we determine for relatively minimal elliptic surfaces with positive Euler number the image of the natural representation of the group of orientation preserving self-diffeomorphisms on $\Hbar$, the second homology group reduced modulo torsion. To this end we construct as many embedded spheres of square -2 ...
1995-07-07
2008-02-03
[ "alg-geom", "math.AG" ]
Michael L"onne
alg-geom/9507004
On a class of rational cuspidal plane curves
We obtain new examples and the complete list of the rational cuspidal plane curves $C$ with at least three cusps, one of which has multiplicity ${\rm deg}\,C - 2$. It occurs that these curves are projectively rigid. We also discuss the general problem of projective rigidity of rational cuspidal plane curves.
1995-07-07
2008-02-03
[ "alg-geom", "math.AG" ]
H. Flenner and M. Zaidenberg
alg-geom/9507002
The line bundles on the stack of parabolic $G$-bundles over curves and their sections
Let $X$ be a smooth, complete and connected curve and $G$ be a simple and simply connected algebraic group over $\comp$. We calculate the Picard group of the moduli stack of quasi-parabolic $G$-bundles and identify the spaces of sections of its members to the conformal blocs of Tsuchiya, Ueno and Yamada. We describe th...
1995-07-05
2008-02-03
[ "alg-geom", "math.AG" ]
Yves Laszlo and Christoph Sorger
alg-geom/9507001
General n-canonical divisors on two-dimensional smoothable semi-log-terminal singularities
In this paper we calculate genaral n-canonical divisors on smoothable semi-log-terminal singularities in dimension 2, in other words, the full sheaves associated to the double dual of the nth tensor power of the dualizing sheaves of these singularities. And as its application we give the inequality which bound the Gore...
1995-07-04
2008-02-03
[ "alg-geom", "math.AG" ]
Masayuki Iwamoto
alg-geom/9506026
On triple coverings of irrational curves
Given a triple covering $X$ of genus $g$ of a general (in the sense of Brill-Noether) curve $C$ of genus $h$, we show the existence of base-point-free pencils of degree $d$ which are not composed with the triple covering for any $d\ge g-[{3h+1\over 2}]-1$ by utilizing some enumerative methods and computations. We also ...
1995-07-03
2008-02-03
[ "alg-geom", "math.AG" ]
Takao Kato, Changho Keem and Akira Ohbuchi
alg-geom/9506025
Automorphisms of crepant resolutions for quotient spaces
A formula for calculating the Lefschetz number of an automorphism acting on a crepant resolution for a quotient of a Kahler manifold derived from an equivariant version of McKay correspondence. The latter is proven in some cases. As an application the Lefschetz numbers of of involutions acting on Calabi-Yau threefolds ...
1995-06-29
2008-02-03
[ "alg-geom", "math.AG" ]
A.Libgober
alg-geom/9506024
Residues in Toric Varieties
We study residues on a complete toric variety X, which are defined in terms of the homogeneous coordinate ring of X. We first prove a global transformation law for toric residues. When the fan of the toric variety has a simplicial cone of maximal dimension, we can produce an element with toric residue equal to 1. We al...
1995-06-27
2008-02-03
[ "alg-geom", "math.AG" ]
Eduardo Cattani, David Cox, and Alicia Dickenstein
alg-geom/9506023
Stacks of Stable Maps and Gromov-Witten Invariants
We correct some errors in the earlier version of this paper. Most importantly, the definition of isogeny of marked stable graphs has changed.
1995-06-27
2008-02-03
[ "alg-geom", "math.AG" ]
K. Behrend and Yu. Manin
alg-geom/9506021
A Vector Bundle of Rank 2 on P1 x P3
The paper studies a rank 2 vector bundle on P1 x P3. Similarly to the Horrocks - Mumford bundle on P4 this vector bundle encodes a lot of geometric information. It is defined via the Serre construction by an abelian surface in P1 x P3. The bundle is stable with respect to O(1,1), its jumping lines are determined. Morov...
1995-06-26
2015-06-30
[ "alg-geom", "math.AG" ]
H. Lange
alg-geom/9506020
Instantons and affine algebras I: The Hilbert scheme and vertex operators
This is the first in a series of papers which describe the action of an affine Lie algebra with central charge $n$ on the moduli space of $U(n)$-instantons on a four manifold $X$. This generalises work of Nakajima, who considered the case when $X$ is an ALE space. In particular, this describes the combinatorial complex...
1995-06-25
2015-06-30
[ "alg-geom", "hep-th", "math.AG" ]
I. Grojnowski (Yale)
alg-geom/9506017
Minimal Siegel modular threefolds
In this paper we study the maximal extension $\Gamma_t^*$ of the subgroup $\Gamma_t$ of $\operatorname{Sp}_4 (\bq)$ which is conjugate to the paramodular group. The index of this extension is $2^{\nu(t)}$ where $\nu(t)$ is the number of prime divisors of $t$. The group $\Gamma_t^*$ defines the minimal modular threefold...
1995-06-23
2008-02-03
[ "alg-geom", "math.AG" ]
Valeri Gritsenko and Klaus Hulek
alg-geom/9506018
Modular forms and Donaldson invariants for 4-manifolds with $b_+=1$
We study the Donaldson invariants of simply connected $4$-manifolds with $b_+=1$, and in particular the change of the invariants under wall-crossing. We assume the conjecture of Kotschick and Morgan about the shape of the wall-crossing terms (which Oszva\'th and Morgan are now able to prove), and are determine a genera...
1995-06-23
2008-02-03
[ "alg-geom", "math.AG" ]
Lothar G\"ottsche
alg-geom/9506019
Wall-crossing formulas, Bott residue formula and the Donaldson invariants of rational surfaces
We study the Donaldson invariants of rational surfaces and their dependence on the chambers in the ample cone. We build on a previous joint paper in which we have expressed the change of the Donaldson invariants on an algebraic surface $S$ under crossing a so-called good wall in terms of certain intersection numbers on...
1995-06-23
2008-02-03
[ "alg-geom", "math.AG" ]
Geir Ellingsrud and Lothar G\"ottsche
alg-geom/9506016
Cycles alg\'ebriques sur les surfaces K3 r\'eelles
For a real algebraic K3 surface $X(R)$, we give all possible values of the dimension $h^1_{alg}(X(R)$ of the group $\H^1_{alg}(X(R),Z/2)$ of algebraic cycles of $X(R)$. In particular, we prove that if $X(R)$ is not an M-surface, $X(R)$ can always be deformed to some $X'(R)$ with $h^1_{alg}(X'(R))=\dim\H^1(X(R),Z/2)$. F...
1995-06-21
2025-05-23
[ "alg-geom", "math.AG" ]
Fr\'ed\'eric Mangolte
alg-geom/9506015
On the separate algebraicity along the families of algebraic curves
A new generalization of the classical separate algebraicity theorem is suggested and proved.
1995-06-21
2008-02-03
[ "alg-geom", "math.AG" ]
R.A.Sharipov and E.N.Tzyganov (Department of Mathematics, Bashkir State University, Russia)
alg-geom/9506013
Fundamental group of locally symmetric varieties
Take a bounded symmetric domain $D$ and an arithmetic subgroup $\Gamma$ of ${\rm Aut}(D)$. Take the quotient $D/\Gamma$, compactify and resolve the singularities. We study the fundamental group of the compact complex manifolds that result from this procedure, and in particular the case of Siegel modular threefolds.
1995-06-20
2008-02-03
[ "alg-geom", "math.AG" ]
G.K. Sankaran
alg-geom/9506014
Higher cohomology triples and holomorphic extensions
We introduce equations for special metrics, and notions of stability for some new types of augmented holomorphic bundles. These new examples include holomorphic extensions, and in this case we prove a Hitchin-Kobayashi correspondence between a certain deformation of the Hermitian-Einstein equations and our definition o...
1995-06-20
2008-02-03
[ "alg-geom", "math.AG" ]
Steven B. Bradlow and Oscar Garcia-Prada
alg-geom/9506012
Semiorthogonal decomposition for algebraic varieties
A criterion for a functor between derived categories of coherent sheaves to be full and faithful is given. A semiorthogonal decomposition for the derived category of coherent sheaves on the intersection of two even dimensional quadrics is obtained. The behaviour of derived categories with respect to birational transfor...
1995-06-19
2008-02-03
[ "alg-geom", "math.AG" ]
A.Bondal and D.Orlov
alg-geom/9506011
Stability of the Poincar\'e bundle
Let $C$ be a nonsingular projective curve of genus $g\ge2$ defined over the complex numbers, and let $M_{\xi}$ denote the moduli space of stable bundles of rank $n$ and determinant $\xi$ on $C$, where $\xi$ is a line bundle of degree $d$ on $C$ and $n$ and $d$ are coprime. It is shown that the universal bundle $\cu_{\x...
1995-06-15
2008-02-03
[ "alg-geom", "math.AG" ]
V. Balaji, L. Brambila Paz, and P. E. Newstead
alg-geom/9506010
Rang maximal pour $T_P^n$
In this paper, I compute the last non-trivial term of the minimal free resolution of the homogeneous ideal of $s$ points of $P^n$ in sufficiently general position, for any $s$, showing that this term is the one conjectured by the Minimal Resolution Conjecture of Anna Lorenzini. I use a geometrical method, the "vectoria...
1995-06-12
2008-02-03
[ "alg-geom", "math.AC", "math.AG" ]
Francois Lauze
alg-geom/9506009
Curves that change genus can have arbitrarily many rational points
A singular curve over a non-perfect field K may not have a smooth model over K. Those are said to "change genus". If K is a global field of positive characteristic and C/K a curve that change genus, then C(K) is known to be finite. The purpose of this note is to give examples of curves with fixed relative genus, define...
1995-06-06
2008-02-03
[ "alg-geom", "math.AG" ]
Jose' Felipe Voloch
alg-geom/9506008
Hermitian-Einstein Inequalities and Harder-Narasimhan Filtration
Unstable holomorphic bundles can be described algebraically by Harder-Narasimhan filtrations. In this note we show how such filtrations correspond to the existence of special metrics defined by Hermitian-Einstein inequalities.
1995-06-05
2008-02-03
[ "alg-geom", "math.AG" ]
Steven B. Bradlow
alg-geom/9506007
On localization and Riemann-Roch numbers for symplectic quotients
Suppose $(M,\omega)$ is a compact symplectic manifold acted on by a compact Lie group $K$ in a Hamiltonian fashion, with moment map $\mu: M \to \Lie(K)^*$ and Marsden-Weinstein reduction $M_{red} = \mu^{-1}(0)/K$. In this paper, we assume that $M$ has a $K$-invariant K\"ahler structure. In an earlier paper, we proved a...
1995-06-04
2008-02-03
[ "alg-geom", "math.AG" ]
Lisa C. Jeffrey, Frances C. Kirwan
alg-geom/9506004
On Alternative Supermatrix Reduction
We consider a nonstandard odd reduction of supermatrices (as compared with the standard even one) which arises in connection with possible extension of manifold structure group reductions. The study was initiated by consideration of the generalized noninvertible superconformal-like transformations. The features of even...
1995-06-02
2009-10-28
[ "alg-geom", "hep-th", "math.AG" ]
Steven Duplij
alg-geom/9506003
A note on the genus of certain curves over finite fields
We prove the following result which was conjectured by Stichtenoth and Xing: let $g$ be the genus of a projective, irreducible non-singular curve over the finite field $\Bbb F_{q^2}$ and whose number of $\Bbb F_{q^2}$-rational points attains the Hasse-Weil bound; then either $4g\le (q-1)^2$ or $2g=(q-1)q$.
1995-06-02
2008-02-03
[ "alg-geom", "math.AG" ]
Rainer Furhmann and Fernando Torres
alg-geom/9506006
Open problems on open algebraic varieties
This report records a large number of open problems in Affine Algebraic Geometry that were proposed by participants in a Conference on Open Algebraic Varieties at the Centre de Recherches en Mathematiques in Montreal at December 1994.
1995-06-02
2008-02-03
[ "alg-geom", "math.AG" ]
R.V. Gurjar, Shulim Kaliman, N. Mohan Kumar, Masayoshi Miyanishi, Peter Russell, Fumio Sakai, David Wright, Mikhail Zaidenberg
alg-geom/9506005
On exotic algebraic structures on affine spaces
By an exotic algebraic structure on the affine space ${\bf C}^n$ we mean a smooth affine algebraic variety which is diffeomorphic to ${\bf R}^{2n}$ but not isomorphic to ${\bf C}^n$. This is a survey of the recent developement on the subject, which emphasizes its analytic aspects and points out some open problems.
1995-06-02
2008-02-03
[ "alg-geom", "math.AG" ]
Mikhail Zaidenberg
alg-geom/9506002
The index of $grad f(x,y)$
Let $f(x,y)$ be a real polynomial of degree $d$ with isolated critical points, and let $i$ be the index of $grad f$ around a large circle containing the critical points. An elementary argument shows that $|i| \leq d-1$. In this paper we show that $ i \leq max \{1, d-3 \}$. We also show that if all the level sets of $f$...
1995-06-01
2008-02-03
[ "alg-geom", "math.AG" ]
Alan H. Durfee
alg-geom/9506001
Composite Differentiable Functions
We introduce a new point of view towards Glaeser's theorem on composite $C^\infty$ functions [Ann. of Math. 1963], with respect to which we can formulate a ``$C^k$ composite function property" that is satisfied by all semiproper real analytic mappings. As a consequence, we see that a closed subanalytic set $X$ satisfie...
1995-06-01
2008-02-03
[ "alg-geom", "math.AG" ]
Edward Bierstone, Pierre D. Milman and Wieslaw Pawlucki
alg-geom/9505038
Uniformity of stably integral points on elliptic curves
A common practice in arithmetic geometry is that of generalizing rational points on projective varieties to integral points on quasi-projective varieties. Following this practice, we demonstrate an analogue of a result of L. Caporaso, J. Harris and B. Mazur, showing that the Lang - Vojta conjecture implies a uniform ...
1995-06-01
2008-02-03
[ "alg-geom", "math.AG" ]
Dan Abramovich
alg-geom/9505036
Del Pezzo surfaces over Dedekind schemes
Let S be a Dedekind scheme with fraction field K. We study the following problem: given a Del Pezzo surface X, defined over K, construct a distinguished integral model of X, defined over all of S. We provide a satisfactory answer if S is a smooth complex curve, and a conjectural answer if X is a cubic Del Pezzo surface...
1995-05-31
2008-02-03
[ "alg-geom", "math.AG" ]
Alessio Corti
alg-geom/9505037
Hodge groups of abelian varieties with purely multiplicative reduction
The main result of the paper is that if $A$ is an abelian variety over a subfield $F$ of ${\bold C}$, and $A$ has purely multiplicative reduction at a discrete valuation of $F$, then the Hodge group of $A$ is semisimple. Further, we give necessary and sufficient conditions for the Hodge group to be semisimple. We obtai...
1995-05-31
2015-06-24
[ "alg-geom", "math.AG" ]
A. Silverberg and Yu. G. Zarhin
alg-geom/9505035
Semistable 3-fold flips
We piece together ingredients, which are well known and documented in the literature, into a new proof of the existence of semistable 3-fold flips
1995-05-31
2008-02-03
[ "alg-geom", "math.AG" ]
Alessio Corti
alg-geom/9505033
Symmetric subgroups of rational groups of hermitian type
A rational group of hermitian type is an algebraic group over the rational numbers whose symmetric space is a hermitian symmetric space. We assume such a group $G$ to be given, which we assume is isotropic. Then, for any rational parabolic $P$ in the group $G$, we find a reductive rational subgroup $N$ closely related ...
1995-05-29
2008-02-03
[ "alg-geom", "math.AG" ]
Bruce Hunt
alg-geom/9505032
The fiber of the Griffiths map for the non-hyperelliptic Fano threefolds of genus 6
Among smooth non-rational Fano 3-folds, the non-hyperelliptic Fano 3-fold X(10) of genus 6 has the unique property to admit a non-trivial orbit of birationally isomorphic 3-folds, inside its moduli space. Here we prove that these orbits are, in fact, the same as the fibers of the Griffiths period map for X(10). This le...
1995-05-29
2008-02-03
[ "alg-geom", "math.AG" ]
Atanas Iliev
alg-geom/9505031
Minimal sections of conic bundles
Let the threefold X be a general smooth conic bundle over the projective plane P(2), and let (J(X), Theta) be the intermediate jacobian of X. In this paper we prove the existence of two natural families C(+) and C(-) of curves on X, such that the Abel-Jacobi map F sends one of these families onto a copy of the theta di...
1995-05-29
2008-02-03
[ "alg-geom", "math.AG" ]
Atanas Iliev
alg-geom/9505030
How to tell you're hearing a Calabi-Yau: Universal variations of Hodge structure and local Schottky relations for Calabi-Yau manifolds
A revised version with a number of corrections and refinements.
1995-05-28
2008-02-03
[ "alg-geom", "math.AG" ]
Ziv Ran
alg-geom/9505029
Quaternionic Monopoles
We present the simplest non-abelian version of Seiberg-Witten theory: Quaternionic monopoles. These monopoles are associated with Spin^h(4)-structures on 4-manifolds and form finite-dimensional moduli spaces. On a Kahler surface the quaternionic monopole equations decouple and lead to the projective vortex equation for...
1995-05-27
2009-10-28
[ "alg-geom", "hep-th", "math.AG" ]
Ch. Okonek and A. Teleman
alg-geom/9505028
Flips from semi-stable 4-folds whose degenerate fibers are unions of Cartier divisors which are terminal factorial 3-folds
We shall investigate flipping contractions from a semi-stable 4-fold $X$ whose degenerate fiber is a union of Cartier divisors which are terminal factorial 3-folds. Especially we shall prove that $X$ is smooth along the flipping locus, and that the flip exists for such contractions.
1995-05-26
2008-02-03
[ "alg-geom", "math.AG" ]
Yasuyuki Kachi
alg-geom/9505027
Determinant of Period Integral
Period integrals arise from the comparison between Betti cohomologies and de Rham cohomologies. In this paper, we give a formula for the determinant of period integrals in terms of the canonical pairing between Picard group of rank 1 realizations and relative Chow group. It is compatible with the similar formula for Ga...
1995-05-26
2008-02-03
[ "alg-geom", "math.AG" ]
Takeshi Saito, and Tomohide Terasoma
alg-geom/9505026
On the local geometry of moduli spaces of vector bundles
We give a canonical description of the formal moduli space of a vector bundle on a variety; as an application, we prove the closedness of certain differential forms on moduli corresponding to the trace form on the endomorphism algebra of the bundle.
1995-05-25
2008-02-03
[ "alg-geom", "math.AG" ]
Ziv Ran
alg-geom/9505024
Determinant Bundles, Quillen Metrics, and Mumford Isomorphisms Over the Universal Commensurability Teichm\"uller Space
There exists on each Teichm\"uller space $T_g$ (comprising compact Riemann surfaces of genus $g$), a natural sequence of determinant (of cohomology) line bundles, $DET_n$, related to each other via certain ``Mumford isomorphisms''. There is a remarkable connection, (Belavin-Knizhnik), between the Mumford isomorphisms a...
1995-05-24
2008-02-03
[ "alg-geom", "hep-th", "math.AG" ]
Indranil Biswas, Subhashis Nag, and Dennis Sullivan
alg-geom/9505025
Topological invariants of a fan associated to a toric variety
Associated to a toric variety $X$ of dimension $r$ over a field $k$ is a fan $\Delta$ on $\Bbb R^r$. The fan $\Delta$ is a finite set of cones which are in one-to-one correspondence with the orbits of the torus action on $X$. The fan $\Delta$ inherits the Zariski topology from $X$. In this article some cohomological in...
1995-05-24
2008-02-03
[ "alg-geom", "math.AC", "math.AG" ]
Timothy J. Ford
alg-geom/9505023
A Note On Elliptic Plane Curves With Fixed j-Invariant
Let N_d be the number of degree d, nodal, rational plane curves through 3d-1 points in the complex projective plane. The number of degree d>=3, nodal, elliptic plane curves with a fixed (general) j-invariant through 3d-1 points is found to be {d-1 \choose 2}*N_d.
1995-05-24
2008-02-03
[ "alg-geom", "math.AG" ]
R. Pandharipande
alg-geom/9505021
Rational surfaces in P^4 containing a plane curve
The families of smooth rational surfaces in $\PP^4$ have been classified in degree $\le 10$. All known rational surfaces in $\PP^4$ can be represented as blow-ups of the plane $\PP^2$. The fine classification of these surfaces consists of giving explicit open and closed conditions which determine the configurations of ...
1995-05-23
2008-02-03
[ "alg-geom", "math.AG" ]
Fabrizio Catanese and Klaus Hulek
alg-geom/9505022
A Geometric Invariant Theory Compactification of M_{g,n} Via the Fulton-MacPherson Configuration Space
A compactification over $\overline{M}_g$ of $M_{g,n}$ is obtained by considering the relative Fulton-MacPherson configuration space of the universal curve. The resulting compactification differs from the Deligne-Mumford space $\overline{M}_{g,n}$. In case $n=2$, the compactification constructed here and the Deligne-Mum...
1995-05-23
2008-02-03
[ "alg-geom", "math.AG" ]
R. Pandharipande
alg-geom/9505020
Lang's conjectures, Conjecture H, and uniformity
The purpose of this note is to wish a happy birthday to Professor Lucia Caporaso.* We prove that Conjecture H of Caporaso et. al. ([CHarM], sec. 6) together with Lang's conjecture implies the uniformity of rational points on varieties of general type, as predicted in [CHarM]; a few applications in arithmetic and geom...
1995-05-21
2015-06-30
[ "alg-geom", "math.AG" ]
Dan Abramovich
alg-geom/9505019
Mapping threefolds onto three-quadrics
We prove that the degree of a nonconstant morphism from a smooth projective 3-fold $X$ with N\'{e}ron-Severi group ${\bf Z}$ to a smooth 3-dimensional quadric is bounded in terms of numerical invariants of $X$. In the special case where $X$ is a 3-dimensional cubic we show that there are no such morphisms. The main too...
1995-05-19
2008-02-03
[ "alg-geom", "math.AG" ]
Carmen Schuhmann