id large_stringlengths 9 16 | title large_stringlengths 1 382 | abstract large_stringlengths 3 6.09k | publish_date date32 | update_date date32 | categories large listlengths 1 13 | authors large_stringlengths 3 62.8k |
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alg-geom/9505018 | Rational Blowdowns of Smooth 4-Manifolds | In this paper we introduce a surgical procedure, called a rational blowdown,
for a smooth 4-manifold X and determine how this procedure affects both the
Donaldson and Seiberg-Witten invariants of X. | 1995-05-17 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Ronald Fintushel and Ronald Stern |
alg-geom/9505017 | On projective plane curves whose complements have finite non-abelian
fundamental groups | We construct new examples of singular projective plane curves whose
complements have finite and non-abelian fundamental groups, by generalizing the
classical three cuspidal quartic curve discovered by Zariski. | 1995-05-15 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Ichiro Shimada |
alg-geom/9505016 | Iitaka-Severi's Conjecture for Complex Threefolds | We prove the following generalization of Severi's Theorem: Let $X$ be a fixed
complex variety. Then there exist, up to birational equivalence, only finitely
many complex varieties $Y$ of general type of dimension at most three which
admit a dominant rational map $f$ from $X$ to Y$. | 1995-05-12 | 2014-12-02 | [
"alg-geom",
"math.AG"
] | Gerd Dethloff |
alg-geom/9505015 | Stratified Picard--Lefschetz theory | The monodromy action in the homology of level sets of Morse functions on
stratified singular analytic varieties is studied. The local variation
operators in both the standard and the intersection homology groups defined by
the loops around the critical values of such functions are reduced to similar
operators in the ho... | 1995-05-11 | 2015-06-30 | [
"alg-geom",
"dg-ga",
"math.AG",
"math.DG"
] | Victor Vassiliev |
alg-geom/9505010 | Algebraic Barth-Lefschetz theorems | Using results of Hironaka-Matsumura and Faltings, we prove a strong version
of the well known Fulton-Hansen connectivity theorem for weighted projective
spaces. As a consequence we get the following result. If $Y$ is an irreducible
subvariety of the $n$-dimensional projective space (over a field of arbitrary
characteri... | 1995-05-08 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Lucian Badescu |
alg-geom/9505014 | Seiberg-Witten Invariants and Rationality of Complex Surfaces | The purpose of this paper is: 1) to explain the Seiberg-Witten invariants, 2)
to show that - on a K\"ahler surface - the solutions of the monopole equations
can be interpreted as algebraic objects, namely effective divisors, 3) to give
- as an application - a short selfcontained proof for the fact that rationality
of c... | 1995-05-08 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Andrei Teleman and Christian Okonek |
alg-geom/9505011 | Les Invariants de Seiberg-Witten et la Conjecture de Van De Ven | We give a short proof for the fact that rationality of complex surfaces is a
property depending only on the differential structure. Our proof uses the new
Seiberg-Witten invariants. | 1995-05-08 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Ch. Okonek, A. Teleman |
alg-geom/9505012 | The Coupled Seiberg-Witten Equations, vortices, and Moduli spaces of
stable pairs | We introduce coupled Seiberg-Witten equations, and we prove, using a
generalized vortex equation, that, for Kaehler surfaces, the moduli space of
solutions of these equations can be identified with a moduli space of
holomorphic stable pairs. In the rank 1 case, one recovers Witten's result
identifying the space of irre... | 1995-05-08 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Ch. Okonek, and A. Teleman |
alg-geom/9505013 | Seiberg-Witten Invariants and the Van De Ven Conjecture | The purpose of this note is to give a short, selfcontained proof of the
following result: A complex surface which is diffeomeorphic to a rational
surface is rational. | 1995-05-08 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Andrei Teleman and Christian Okonek |
alg-geom/9505009 | Spectral Covers | This is a survey of various results about spectral covers and their
relationship to Higgs bundles. To a G-principal Higgs bundle on a variety S
corresponds a cameral cover \widetilde{S} of S (a W-Galois cover, where W is
the Weyl group of G) together with a sheaf on \widetilde{S} which in simple
cases is a line bundle,... | 1995-05-07 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Ron Donagi |
alg-geom/9505007 | A note on Zariski pairs | A couple of complex projective plane curves are said to make a Zariski pair
if they have the same degree and the same type of singularities, but their
embeddings in the projective plane are topologically different. In this paper,
we present a method to construct certain type of Zariski pairs, and make
infinite series o... | 1995-05-05 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Ichiro Shimada |
alg-geom/9505008 | Un crit\`ere d'extension d'un foncteur d\'efini sur les sch\'emas lisses | Let $k$ be a field of characteristic zero. By using Hironaka's
desingularisation theorem, we prove an extension criterion for a functor
defined on nonsingular k-schemes and taking values on a category of complexes.
Roughly speaking, the criterion shows that if such a functor satisfies the
standard exact sequence of a b... | 1995-05-05 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | F. Guill\'en and V. Navarro Aznar |
alg-geom/9505005 | Sequences of stable bundles over a compact complex surface | When identified with sequences of irreducible Hermitian-Einstein connections,
sequences of stable holomorphic bundles of fixed topological type and bounded
degree on a compact complex surface equipped with a Gauduchon metric are shown
to have strongly convergent subsequences after blowing-up and pulling-back
sufficient... | 1995-05-05 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Nicholas P. Buchdahl |
alg-geom/9505006 | Blowups and gauge fields | The relationship between stable holomorphic vector bundles on a compact
complex surface and the same such objects on a blowup of the surface is
investigated, where "stability" is with respect to a Gauduchon metric on the
surface and naturally derived such metrics on the blowup.
The main results are: descriptions of h... | 1995-05-05 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Nicholas P. Buchdahl |
alg-geom/9505004 | A weighted version of Zariski's hyperplane section theorem and
fundamental groups of complements of plane curves | We formulate and prove a weighted version of Zariski's hyperplane section
theorem on the topological fundamental groups of the complements of
hypersurfaces in a projective space. As an application, we calculate
fundamental groups of the complements of certain singular projective plane
curves. | 1995-05-04 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Ichiro Shimada |
alg-geom/9505003 | Bogomolov conjecture over function fields for stable curves with only
irreducible fibers (Version 2.0) | Let K be a function field and C a non-isotrivial curve of genus g >= 2 over
K. In this paper, we will show that if C has a global stable model with only
geometrically irreducible fibers, then Bogomolov conjecture over function
fields holds. | 1995-05-04 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Atsushi Moriwaki |
alg-geom/9505002 | Quantum cohomology of flag varieties | We describe a construction of Gromov-Witten invariants for flag varieties and
use it to give a presentation for the quantum cohomology ring, by extending the
ideas used by Bertram in the case of Grassmannians. This provides a proof for
the conjecture of Givental and Kim in [GK]. | 1995-05-03 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Ionu\c{t} Ciocan-Fontanine |
alg-geom/9505001 | Pieri's rule for flag manifolds and Schubert polynomials | We establish the formula for multiplication by the class of a special
Schubert variety in the integral cohomology ring of the flag manifold. This
formula also describes the multiplication of a Schubert polynomial by either an
elementary symmetric polynomial or a complete homogeneous symmetric polynomial.
Thus, we gener... | 1995-05-02 | 2008-02-03 | [
"alg-geom",
"math.AG",
"math.CO"
] | Frank Sottile |
alg-geom/9504017 | A Non-Linear Deformation of the Hitchin Dynamical System | Mukai's space, parametrizing simple sheaves on a K3 surface S whose numerical
invariants are those of a line bundle on a curve C in S, is interpreted as a
deformation of Hitchin's system on C. This is used to show that the nilpotent
cone in Mukai space is Lagrangian. In rank 2, components of this nilpotent cone
are des... | 1995-04-30 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Ron Donagi, Lawrence Ein and Robert Lazarsfeld |
alg-geom/9504016 | Gauge fixing for logarithmic connections over curves and the
Riemann-Hilbert-Problem | We explain in detail the correspondence between algebraic connections over
CP^{1}, logarithmic at X = { x_{1},...,x_{n} } \subset CP^{1}, and flat bundles
over CP^{1}-X with integer weighted filtrations near each x_{j}. Included is a
gauge fixing theorem for logarithmic connections. (Thus far, one could work
over any R... | 1995-04-29 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Christian Gantz and Brian Steer |
alg-geom/9504015 | Orbifold Riemann Surfaces and the Yang-Mills-Higgs Equations | We extend Hitchin's results on "The self-duality equations on a Riemann
surface" (Proc. LMS (3), vol. 55, 1987) to orbifold Riemann surfaces. We prove
existence results for orbifold solutions of the Yang-Mills-Higgs equations and
construct the moduli space of solutions. These moduli spaces provide
interesting examples ... | 1995-04-26 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Ben Nasatyr and Brian Steer |
alg-geom/9504014 | Relative Geometric Invariant Theory and Universal Moduli Spaces | We expose in detail the principle that the relative geometric invariant
theory of equivariant morphisms is related to the GIT for linearizations near
the boundary of the $G$-effective ample cone. We then apply this principle to
construct and reconstruct various universal moduli spaces. In particular, we
constructed the... | 1995-04-25 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Yi Hu |
alg-geom/9504013 | Making enumerative predictions by means of mirror symmetry | Given two Calabi--Yau threefolds which are believed to constitute a mirror
pair, there are very precise predictions about the enumerative geometry of
rational curves on one of the manifolds which can be made by performing
calculations on the other. We review the mechanics of making these predictions,
including a discus... | 1995-04-24 | 2008-02-03 | [
"alg-geom",
"hep-th",
"math.AG"
] | David R. Morrison |
alg-geom/9504012 | On irreducible four--manifolds | We show that minimal symplectic 4--manifolds with $b_2^+ >1$ and with
residually finite fundamental groups are irreducible. We also give examples of
irreducible orientable four--manifolds with indefinite intersection forms which
are not almost complex with respect to either orientation. | 1995-04-23 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | D. Kotschick |
alg-geom/9504011 | Picard groups of the moduli spaces of vector bundles over algebraic
surfaces | We determined the Picard group of the moduli of rank two stable sheaves on an
arbitrary algebraic surface up to finite index | 1995-04-16 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Jun Li |
alg-geom/9504009 | The quantum cohomology of homogeneous varieties | We established the associativity of the quantum cohomologies of homogeneous
varieties by using degeneration method in algebraic geometry. | 1995-04-16 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Jun Li and Gang Tian |
alg-geom/9504010 | The first two Betti numbers of the moduli spaces of vector bundles on
surfaces | We determined the first two Betti numbers of the moduli of rank two stable
sheaves on an arbitrary algebraic surface | 1995-04-16 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Jun Li |
alg-geom/9504008 | Integral Subschemes of Codimension Two | In this paper we study the problem of describing the integral subschemes
within a fixed even linkage class $\L$ of subschemes in $\Pn$ of codimension
two. In the case that $\L$ is not the class of arithmetically Cohen-Macaulay
subschemes, we associate to any $X \in \L$ two invariants $\theta_X$ and
$\eta_X$. When taken... | 1995-04-15 | 2015-06-30 | [
"alg-geom",
"math.AC",
"math.AG"
] | Scott Nollet |
alg-geom/9504007 | Some Donaldson invariants of CP^2 | We compute the Donaldson numbers $q_{17}(CP^2)=2540$ and
$q_{21}(CP^2)=233208$. | 1995-04-13 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Geir Ellingsrud, Joseph Le Potier, and Stein A. Stromme |
alg-geom/9504006 | Siegel automorphic form corrections of some Lorentzian Kac--Moody Lie
algebras | We find automorphic form corrections which are generalized Lorentzian
Kac--Moody superalgebras without odd real simple roots (see R. Borcherds
\cite{Bo1} -- \cite{Bo7}, V. Kac \cite{Ka1} -- \cite{Ka3}, R. Moody \cite{Mo}
and \S~6 of this paper) for two elliptic Lorentzian Kac--Moody algebras of the
rank $3$ with a latt... | 1995-04-10 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Valeri A. Gritsenko and Viacheslav V. Nikulin |
alg-geom/9504005 | Intersection-theoretical computations on \Mgbar | We determine necessary conditions for ample divisors in arbitrary genus as
well as for very ample divisors in genus 2 and 3. We also compute the
intersection numbers $\lambda^9$ and $\lambda_{g-1}^3$ in genus 4. The latter
number is relevant for counting curves of higher genus on manifolds, cf. the
recent work of Bersh... | 1995-04-06 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Carel Faber |
alg-geom/9504003 | Severi Degrees in Cogenus 3 | In this short note, a new computation of the degree of the locus of 3-nodal
plane curves in the linear system of degree d plane curves is given. The answer
is expressed as a tautological class on a blow-up of the Hilbert scheme of 3
points in the plane. The class is evaluated by the Bott residue formula. | 1995-04-06 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | J. Harris and R. Pandharipande |
alg-geom/9504004 | Intersections of Q-Divisors on Kontsevich's Moduli Space
$\bar{M}_{0,n}(P^r,d)$ and Enumerative Geometry | The theory of Q-Cartier divisors on the space of n-pointed, genus 0, stable
maps to projective space is considered. Generators and Picard numbers are
computed. A recursive algorithm computing all top intersection products of
Q-Divisors is established. As a corollary, an algorithm computing all
characteristic numbers of... | 1995-04-06 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | R. Pandharipande |
alg-geom/9504002 | On number of hypersurfaces containing projective curves | Generalizing a classical lemma of Castelnuovo, we characterize rational
normal curves (resp. linearly normal elliptic curves) as curves $C\subset
\PP^n$ such that the number of linearly independent hypersurfaces $Z\supset C$
of given degree~$m$ is maximal (resp. next to maximal). | 1995-04-04 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | S. L'vovsky |
alg-geom/9504001 | Hyperbolic Planes | In this paper we consider a special class of arithmetic quotients of bounded
symmetric domains which can roughly be described as higher- dimensional
analogues of the Hilbert modular varities. The algebraic groups are defined as
the unitary groups over two-dimensional right vector spaces over a division
algebra with inv... | 1995-04-03 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Bruce Hunt |
alg-geom/9503025 | Local Homology and Cohomology on Schemes | We prove a sheaf-theoretic derived-category generalization of Greenlees-May
duality (a far-reaching generalization of Grothendieck's local duality
theorem): for a quasi-compact separated scheme X and a "proregular" subscheme
Z---for example, any separated noetherian scheme and any closed
subscheme---there is a sort of ... | 1995-03-30 | 2008-02-03 | [
"alg-geom",
"math.AC",
"math.AG"
] | Leovigildo Alonso, Ana Jerem\'ias, and Joseph Lipman |
alg-geom/9503024 | Degrees of generators of ideals defining subschemes of projective space | For an arithmetically Cohen--Macaulay subscheme of projective space, there is
a well-known bound for the highest degree of a minimal generator for the
defining ideal of the subscheme, in terms of the Hilbert function. We prove a
natural extension of this bound for arbitrary locally Cohen--Macaulay
subschemes. We then s... | 1995-03-29 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Heath M. Martin and Juan C. Migliore |
alg-geom/9503022 | Roitman's theorem for singular complex projective surfaces | Let $X$ be a complex projective surface with arbitrary singularities. We
construct a generalized Abel--Jacobi map $A_0(X)\to J^2(X)$ and show that it is
an isomorphism on torsion subgroups. Here $A_0(X)$ is the appropriate Chow
group of smooth 0-cycles of degree 0 on $X$, and $J^2(X)$ is the intermediate
Jacobian assoc... | 1995-03-29 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | L. Barbieri-Viale, C. Pedrini and C. Weibel |
alg-geom/9503023 | The Mumford relations and the moduli of rank three stable bundles | We find a complete set of relations for the rational cohomology ring of the
moduli space of rank three stable bundles over a Riemann surface of genus g and
also show that the Pontryagin ring vanishes in degree 12g-8 and greater. The
results are obtained by introducing some 'dual' Mumford relations and
generalising Kirw... | 1995-03-29 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Richard Earl |
alg-geom/9503020 | Th\'eor\`emes De Connexit\'e Pour Les Produits D'Espaces Projectifs et
Les Grassmanniennes | Let $G$ be the Grassmannian $G(d,n)$, let $X$ and $Y$ be complete irreducible
varieties, and let $X\rightarrow G$ and $Y\rightarrow G$ be morphisms. Hansen
proved that $X \times_G Y$ is connected when $codim f(X) + codim g(Y) < n$. We
show that the conclusion holds under the often weaker hypothesis
$f(X).g(Y).T\ne 0$, ... | 1995-03-28 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Olivier Debarre |
alg-geom/9503021 | Moduli of pre-$\cal D$-modules, perverse sheaves and the Riemann-Hilbert
morphism -I | We construct a moduli scheme for semistable pre-$\D$-modules with prescribed
singularities and numerical data on a smooth projective variety. These
pre-$\D$-modules are to be viewed as regular holonomic $\D$-modules with `level
structure'. We also construct a moduli scheme for perverse sheaves on the
variety with presc... | 1995-03-28 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Nitin Nitsure and Claude Sabbah |
alg-geom/9503018 | A gem of the modular universe | We introduce one of the most beautiful algebraic varieties known, a quintic
hypersurface in projective five-space, which is invariant under the action of
the Weyl group of $E_6$. This variety is intricately related with many other
moduli problems, some of which are: marked hyperelliptic curves of genus two,
Picard curv... | 1995-03-27 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Bruce Hunt |
alg-geom/9503019 | An orbifold partition of ${\overline{M}_g^n}$ | We define a partition of ${\overline{M}_g^n}$ and show that the cohomology of
${\overline{M}_g^n}$ in a given degree admits a filtration whose respective
quotients are isomorphic to the shifted cohomology groups of the parts if $g$
is sufficiently large. This implies that the map $H^k({\overline{M}_g^n}) \ra
H^k(M_g^n)... | 1995-03-27 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Martin Pikaart |
alg-geom/9503017 | Akizuki's counterexample | Following Akizuki, I construct a Noetherian local integral domain C_M whose
normalisation (integral closure) is not finite over C_M. My proof follows
closely Akizuki's ingenious calculations. | 1995-03-26 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Miles Reid |
alg-geom/9503016 | On a conjecture of Varchenko | In this note we generalize and prove a recent conjecture of Varchenko
concerning the number of critical points of a (multivalued) meromorphic
function $\phi$ on an algebraic manifold. Under certain conditions, this number
turns out to coincide with the Euler characteristic (up to a sign) of the
complement of the diviso... | 1995-03-26 | 2009-10-28 | [
"alg-geom",
"math.AG"
] | Roberto Silvotti |
alg-geom/9503015 | The nil Hecke ring and singularity of Schubert varieties | We give a criterion for smoothness of a point in any Schubert variety in any
G/B in terms of the nil Hecke ring. | 1995-03-24 | 2015-06-24 | [
"alg-geom",
"math.AG"
] | Shrawan Kumar |
alg-geom/9503013 | Moduli spaces of semiquasihomogeneous singularities with fixed principal
part | We construct coarse moduli spaces of semiquasihomogeneous hypersurface
singularities with respect to right equivalence and contact equivalence. We
have to fix the principal part of the semiquasihomogeneous singularities. For
the moduli spaces with respect to contact equivalence we also fix the Hilbert
function of the T... | 1995-03-22 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | G.-M. Greuel, C. Hertling, and G. Pfister |
alg-geom/9503014 | Stable Parabolic Bundles over Elliptic Surfaces and over Orbifold
Riemann Surfaces | For an elliptic surface $q:Y \to \Sigma$, with prescribed singular fibres,
Stefan Bauer proved directly via algebraic geometry that the stable bundles
over $Y$, whose chern classes are pull backs from $\Sigma$, correspond to the
stable (V-)bundles over $\Sigma$.
We show, via a short proof in differential geometry, a ... | 1995-03-22 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Christian Gantz and Brian Steer |
alg-geom/9503012 | The irreducibility of the moduli space of stable vector bundles of rank
2 on a quintic in $\pp^3$ | In this paper I consider a quintic surface in $\pp^3$, general in the sense
of Noether-Lefschetz theory. The vector bundles of rank 2 on this surface which
are $\mu$-stable with respect to the hyperplane section and have $c_1 = K$, the
canonical class of the surface and fixed $c_2$, are parametrized by a moduli
space. ... | 1995-03-22 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Pieter Nijsse |
alg-geom/9503011 | Equianalytic and equisingular families of curves on surfaces | We consider flat families of reduced curves on a smooth surface S such that
each member C has the same number of singularities of fixed singularity types
and the corresponding (locally closed) subscheme H of the Hilbert scheme of S.
We are mainly concerned with analytic resp. topological singularity types and
give a su... | 1995-03-21 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Gert-Martin Greuel, Christoph Lossen |
alg-geom/9503010 | Hitchin systems, higher Gaudin operators and $r$-matrices | We adapt Hitchin's integrable systems to the case of a punctured curve. In
the case of $\CC P^{1}$ and $SL_{n}$-bundles, they are equivalent to systems
studied by Garnier. The corresponding quantum systems were identified by B.
Feigin, E. Frenkel and N. Reshetikhin with Gaudin systems. We give a formula
for the higher ... | 1995-03-20 | 2015-06-30 | [
"alg-geom",
"hep-th",
"math.AG",
"nlin.SI",
"solv-int"
] | B. Enriquez and V. Rubtsov |
alg-geom/9503009 | Geometric Properties of the Double-Point Divisor | Let $X^n \subset P^N$ be a nonsingular, nondegenerate projective variety of
dimension $n$ and codimension $N-n \ge 2$. Let $|C_X|$ be the linear system
determined by the double-point divisor obtained by generically projecting $X$
to a hypersurface in $P^{n+1}$. We classify those varieties for which $C_X$ is
not ample, ... | 1995-03-17 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Bo Ilic |
alg-geom/9503008 | Bloch's conjecture revisited | Let $X$ be a non-singular projective complex surface. We can show that
Bloch's conjecture (i.e., that if $p_g=0$ then the Albanese kernel vanishes) is
equivalent to the following statement: If $p_g(X)=0$ then for any given Zariski
open $U\subset X$ and $\omega\in H^2(U,{\bf C})$ there is a smaller Zariski
open $V\subse... | 1995-03-16 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | L. Barbieri-Viale and V. Srinivas |
alg-geom/9503007 | Quotient Spaces Modulo Algebraic Groups | The paper proves that if a reductive group scheme acts properly on a scheme
then the geometric quotient exists as an algebraic space. As a consequence we
obtain the existence of the moduli spcace of canonically polarized varieties
over Spec Z. | 1995-03-16 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | J\'anos Koll\'ar |
alg-geom/9503006 | The Langlands lemma and the Betti numbers of stacks of $G$--bundles on a
curve | In this note we show that the Langlands lemma from the theory of Eisenstein
series can be used to invert the recursion relation for the Poincar\'e series
of the open substack of semi-stable $G$-bundles which was established by
Atiyah/Bott and Harder/Narasimhan. | 1995-03-14 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | G. Laumon, and M. Rapoport |
alg-geom/9503005 | An algebraic version of Demailly's asymptotic Morse Inequalities | We give an elementary algebraic proof of some asymptotic estimates (called by
Demailly asymptotic Morse inequalities) for the dimensions of cohomology groups
of the difference of two ample line bundles on a smooth complex projective
variety of any dimension. | 1995-03-14 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Flavio Angelini |
alg-geom/9503004 | The canonical class and the $C^\infty$ properties of K\"ahler surfaces | We give a self contained proof using Seiberg Witten invariants that for
K\"ahler surfaces with non negative Kodaira dimension (including those with
$p_g = 0$) the canonical class of the minimal model and the $(-1)$-curves, are
oriented diffeomorphism invariants up to sign. This implies that the Kodaira
dimension is det... | 1995-03-10 | 2008-02-03 | [
"alg-geom",
"dg-ga",
"math.AG",
"math.DG"
] | Rogier Brussee |
alg-geom/9503003 | Reflection groups in hyperbolic spaces and the denominator formula for
Lorentzian Kac--Moody Lie algebras | This is a continuation of our "Lecture on Kac--Moody Lie algebras of the
arithmetic type" \cite{25}.
We consider hyperbolic (i.e. signature $(n,1)$) integral symmetric bilinear
form $S:M\times M \to {\Bbb Z}$ (i.e. hyperbolic lattice), reflection group
$W\subset W(S)$, fundamental polyhedron $\Cal M$ of $W$ and an ac... | 1995-03-10 | 2015-06-24 | [
"alg-geom",
"hep-th",
"math.AG",
"math.QA",
"q-alg"
] | Viacheslav V. Nikulin |
alg-geom/9503002 | Homology of iterated semidirect products of free groups | Let $G$ be a group which admits the structure of an iterated semidirect
product of finitely generated free groups. We construct a finite, free
resolution of the integers over the group ring of $G$. This resolution is used
to define representations of groups which act compatibly on $G$, generalizing
classical constructi... | 1995-03-07 | 2007-07-02 | [
"alg-geom",
"math.AG"
] | Daniel C. Cohen and Alexander I. Suciu |
alg-geom/9503001 | Quasi-parabolic Siegel Formula | The result of Siegel that the Tamagawa number of $SL_r$ over a function field
is 1 has an expression purely in terms of vector bundles on a curve, which is
known as the Siegel formula. We prove an analogous formula for vector bundles
with quasi-parabolic structures. This formula can be used to calculate the
Betti numbe... | 1995-03-02 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Nitin Nitsure |
alg-geom/9502027 | On the blowups of numerical Godeaux surfaces | We give a short proof of the following result: Let $X$ be a complex surface
of general type. If the canonical divisor of the minimal model of $X$ has
selfintersection $= 1$, then $X$ is not diffeomorphic to a rational surface.
Our proof is the natural extension of the argument given in our paper in
Inventiones Mathemat... | 1995-03-01 | 2010-06-03 | [
"alg-geom",
"math.AG"
] | D. Kotschick |
alg-geom/9502028 | Non--trivial harmonic spinors on generic algebraic surfaces | We disprove Hitchin's conjecture to the effect that for a generic complex
structure on a simply connected spin complex surface the square root of the
canonical bundle has no more cohomology then is predicted by the Riemann--Roch
theorem. (This paper will appear in Proc. Amer. Math. Soc.) | 1995-03-01 | 2010-06-03 | [
"alg-geom",
"math.AG"
] | D. Kotschick |
alg-geom/9502026 | Algebraic surfaces and Seiberg-Witten invariants | In this revised version, we add some expository material and references and
make some minor corrections. | 1995-02-27 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Robert Friedman and John W. Morgan |
alg-geom/9502025 | Linear bound for abelian automorphisms of varieties of general type | We prove: Let $G$ be a finite abelian group acting faithfully on a complex
smooth project variety $X$ of general type with numerically effective canonical
divisor, of dimension $n$. Then
$$|G| \le C(n)K_X^n ,$$
where $C(n)$ depends only on $n$. | 1995-02-27 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Gang Xiao |
alg-geom/9502024 | Traces and Differential Operators over Beilinson Completion Algebras | A Beilinson completion algebra (BCA) A is a complete semilocal algebra over a
perfect field k, whose residue fields are high dimensional local fields. In
addition A is a semi-topological algebra. The completion of the structure sheaf
of an algebraic k-variety along a saturated chain of points is the prototypical
exampl... | 1995-02-26 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Amnon Yekutieli |
alg-geom/9502023 | Extremal contractions from 4-dimensional manifolds to 3-folds | Let $g : X \to Y$ be the contraction of an extremal ray of a smooth
projective 4-fold $X$ such that $\dim Y=3$. Then $g$ may have a finite number
of 2-dimensional fibers. We shall classify those fibers. Especially we shall
prove that any two points of such a fiber is joined by a chain of rational
curves of length at mo... | 1995-02-25 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Yasuyuki Kachi |
alg-geom/9502022 | Torsion-Free Sheaves and Moduli of Generalized Spin Curves | This article treats compactifications of the space of generalized spin
curves. Generalized spin curves, or $r$-spin curves, are pairs $(X,L)$ with $X$
a smooth curve and $L$ a line bundle whose r-th tensor power is isomorphic to
the canonical bundle of $X.$ These are a natural generalization of $2$-spin
curves (algebra... | 1995-02-21 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Tyler J. Jarvis |
alg-geom/9502021 | Koszul Property and Frobenius Splitting of Schubert Varieties | We show how the Frobenius splitting method of Mehta-Ramanathan implies the
Koszul property of projective coordinate rings of Schubert varieties. | 1995-02-20 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Roman Bezrukavnikov |
alg-geom/9502019 | Algebraic cohomology of the moduli space of rank 2 vector bundles on a
curve | Let $\MC$ be the moduli space of stable holomorphic vector bundles of rank 2
and fixed determinant of odd degree, over a smooth projective curve $C$. This
paper identifies the algebraic cohomology ring $\HA^*(\MC)$, i.e. the subring
of the rational cohomology ring $H^*(\MC;\QQ)$ spanned by the fundamental
classes of al... | 1995-02-17 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | V. Balaji, A.D. King and P.E. Newstead |
alg-geom/9502020 | A Compactification Over $\overline{M}_g$ Of The Universal Moduli Space
of Slope-Semistable Vector Bundles | A projective moduli space of pairs (C,E) where E is a slope- semistable
torsion free sheaf of uniform rank on a Deligne- Mumford stable curve C is
constructed via G.I.T. There is a natural SL x SL action on the relative Quot
scheme over the universal curve of the Hilbert scheme of pluricanonical, genus
g curves. The G.... | 1995-02-17 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | R. Pandharipande |
alg-geom/9502015 | Fundamental groups of complements of curves as solvable groups | We discuss the applications of fundamental groups (of complements of curves)
computations (and possibly the computations of the second homotopy group as a
model over it) to the classification of algebraic surface. We prove that the
fundamental group of the complement of the branch curve of a generic projection
of a Ver... | 1995-02-16 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Boris Moishezon and Mina Teicher |
alg-geom/9502016 | Embeddings of homogeneous spaces in prime characteristics | Let $G$ be a reductive linear algebraic group. The simplest example of a
projective homogeneous $G$-variety in characteristic $p$, not isomorphic to a
flag variety, is the divisor $x_0 y_0^p+x_1 y_1^p+x_2 y_2^p=0$ in $P^2\times
P^2$, which is $SL_3$ modulo a non-reduced stabilizer containing the upper
triangular matric... | 1995-02-16 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Niels Lauritzen |
alg-geom/9502017 | Poncelet theorems | If there is one polygon inscribed into some smooth conic and circumscribed
about another one, then there are infinitely many such polygons. This is
Poncelet's theorem. The aim of this note is to collect some (mostly classical)
versions of this theorem, namely:
- Weyr's Poncelet theorem in $P_3$ (1870),
- Emch's the... | 1995-02-16 | 2025-04-09 | [
"alg-geom",
"math.AG"
] | W. Barth, Th. Bauer |
alg-geom/9502018 | On the cohomology ring of the moduli space of rank 2 vector bundles on a
curve | Let $\MS_g$ be the moduli space of stable holomorphic vector bundles of rank
2 and fixed determinant of odd degree over a smooth complex projective curve of
genus $g$. This paper proves various properties of the rational cohomology ring
$H^*(\MS_g)$. It is shown that the first relation in genus $g$ between the
standard... | 1995-02-16 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | A.D. King, P.E. Newstead |
alg-geom/9502014 | Self-intersection of dualizing sheaves of arithmetic surfaces with
reducible fibers | Let K be an algebraic number field and O_K the ring of integers of K. Let f :
X --> Spec(O_K) be a stable arithmetic surface over O_K of genus g >= 2. In
this short note, we will prove that if f has a reducible geometric fiber, then
the self intersection of dualizing sheaf of X with Arakelov metric is greater
than or e... | 1995-02-16 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Atsushi Moriwaki |
alg-geom/9502013 | Abelian automorphism groups of threefolds of general type | This thesis is devoted to the study of abelian automorphism groups of
surfaces and $3$-folds of general type over complex number field $\Bbb C$. We
obtain a linear bound in $K^3$ for abelian automorphism groups of $3$-folds of
general type whose canonical divisor $K$ is numerically effective, and we
improve on Xiao's r... | 1995-02-15 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Jin-Xing Cai |
alg-geom/9502012 | k-very ample line bundles on Del Pezzo Surfaces | A $k$-very ample line bundle L on a Del Pezzo Surface is numerically
characterized. We find that the set of the exceptional curves and effective
divisors with selfintersection zero, $\cal S$, plays a very important rule in
checking the nefness and $k$-very ampleness of a line bundle on a Del pezzo
Surface. We show that... | 1995-02-15 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Sandra Di Rocco |
alg-geom/9502009 | Braid Group techniques in Complex Geometry V: The fundamental group of
the complement of a Veronese generic projection | Computation of the fundamental group of the complement in the complex plane
of the branch curve S , of a generic projection of the Veronese surface to the
plane is presented. This paper is a continuation of our previous papers: Braid
Group Technique I - IV. In I and II we developed algorithms to compute braid
monodromy... | 1995-02-14 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Mina Teicher and Boris Moishezon |
alg-geom/9502011 | Height inequality of algebraic points on curves over functional fields | The purpose of this paper is to give a linear and effective height inequality
for algebraic points on curves over functional fields. Our height inequality
can be viewed as the logarithmic canonical class inequality of a punctured
curve over a functional field (a fibered surface minus a section). | 1995-02-14 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Sheng-Li Tan |
alg-geom/9502010 | Operads, Grothendieck topologies and Deformation theory | The idea of the work is to find an invariant way to pass from deformation
theory to cohomology, which does not use any explicit cocycles. The appropriate
cohomology theory is based on considering sheaves on a certain site. An
advantage of the approach is that it enables one to give a simultanious
treatement to all type... | 1995-02-14 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | D.Gaitsgory |
alg-geom/9502008 | On singularities of ${\cal M}_{I\!\! P^3}(c_1,c_2)$ | Let ${\cal M}_{I\!\! P^3}(c_1,c_2)$ be the moduli space of stable rank-$2$
vector bundles on $I\!\! P^3$ with Chern classes $c_1$, $ c_2$. We prove the
following results.
1) Let $0 \le \beta < \gamma $ be two integers, ($\gamma \ge 2)$, such that
$2\gamma-3\beta>0$; then ${\cal M}_{I\!\! P^3}(0,2\gamma^2-3\beta^2)$ i... | 1995-02-13 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Vincenzo Ancona and Giorgio Ottaviani |
alg-geom/9502007 | Log Sarkisov Program | The purpose of this paper is two-fold. The first is to give a tutorial
introduction to the Sarkisov program, a 3-dimensional generalization of
Castelnuovo-N\"other Theorem ``untwisting" birational maps between Mori fiber
spaces, which was recently established by Corti after Sarkisov and Reid.
The second is an attempt... | 1995-02-10 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Andrea Bruno and Kenji Matsuki |
alg-geom/9502006 | Homology of moduli spaces of curves and commutative homotopy algebras | We propose an explicit relation between the cohomology of compactified and
noncompactified moduli spaces of algebraic curves with punctures. This
relationship generalizes one between commutative algebras and Lie algebras
proposed by Lazard, Kontsevich and Ginzburg and Kapranov. More explicitly, we
show that the cohomol... | 1995-02-08 | 2008-02-03 | [
"alg-geom",
"hep-th",
"math.AG",
"math.QA",
"q-alg"
] | Takashi Kimura, Jim Stasheff, and Alexander A. Voronov |
alg-geom/9502005 | Mirror symmetry for lattice polarized K3 surfaces | We establish a relationship between mirror symmetry for K3 surfaces and
Arnold's strange duality for K3 surfaces. We compute various examples of mirror
families. Among them the mirror moduli family for the moduli space of degree 2n
polarized K3 surfaces. It turns out to be related to the moduli space of
elliptic curves... | 1995-02-07 | 2008-02-03 | [
"alg-geom",
"hep-th",
"math.AG"
] | Igor V. Dolgachev |
alg-geom/9502004 | Duality of Weights, Mirror Symmetry and Arnold's Strange Duality | A notion of duality of weight systems which corresponds to Batyrev's toric
mirror symmetry is given. Explicit duality on the (1,1)-cohomology of K3
surfaces which are minimal models of toric hypersurfaces is constructed using
monomial divisor mirror map of Aspinwall-Greene-Morrison. It is shown that
Arnold's strange du... | 1995-02-06 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Masanori Kobayashi |
alg-geom/9502003 | A Calabi-Yau threefold with non-Abelian fundamental group | The title is self-explanatory. | 1995-02-03 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Arnaud Beauville |
alg-geom/9502002 | A Generalization of the Kodaira Vanishing and Embedding Theorem | We give several generalizations of the Kodaira vanishing and embedding
theorems for K\"ahler manifolds to the case where the relevent line bundle has
a small region of negative curvature. To prove the vanishing theorems we adapt
techniques of Elworthy-Rosenberg for vanishing theorems in Riemannian geometry.
For the emb... | 1995-02-02 | 2015-06-30 | [
"alg-geom",
"dg-ga",
"math.AG",
"math.DG"
] | Ying Zhu |
alg-geom/9502001 | A sextic surface cannot have 66 nodes | Let S be a surface in complex projective 3-space, having only nodes as
singularities. Suppose that S has degree 6. We show that the maximum number of
nodes which S can have is 65.
An abbreviated history of this is as follows. Basset showed that S can have
at most 66 nodes. Catanese and Ceresa and Stagnaro constructed... | 1995-02-01 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | David B. Jaffe and Daniel Ruberman |
alg-geom/9501013 | The motive of some moduli spaces of vector bundles over a curve | We study the motive of the moduli spaces of semistable rank two vector
bundles over an algebraic curve. When the degree is odd the moduli space is a
smooth projective variety, we obtain the absolute Hodge motive of this, and in
particular the Hodge-Poincare polynomial. When the degree is even the moduli
space is a sing... | 1995-01-31 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Sebastian del Bano Rollin |
alg-geom/9501010 | On the tautological ring of $\M _g$ | We prove among other things that any product of tautological classes of
$\M_g$ of degree $d$ (in the Chow ring of $\M _g$ with rational coefficients)
vanishes for $d>g-2$ and is proportional to the class of the hyperelliptic
locus in degree $g-2$. | 1995-01-20 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Eduard Looijenga |
alg-geom/9501011 | Some homogeneous coordinate rings that are Koszul algebras | Using reduction to positive characteristic and the method of Frobenius
splitting of diagonals, due to Mehta and Ramanathan, it is shown that
homogeneous coordinate rings for either proper and smooth toric varieties or
Schubert varieties are Koszul algebras. | 1995-01-20 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Rikard B\"ogvad |
alg-geom/9501012 | On the homogeneous ideal of a projective nonsingular toric variety | Reason for withdrawal:
There is a serious mistake in the calculation of the divisor of the rational
section used in the proof of Prop. 2.2.1., and with the correct value the
argument does not work. | 1995-01-20 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Rikard B\"ogvad |
alg-geom/9501007 | Plane Curves with Hyperbolic and C-hyperbolic Complements | The general problem which initiated this work is:
What are the quasiprojective varieties which can be uniformized by means of
bounded domains in $\cz^n$ ?
Such a variety should be, in particular, C--hyperbolic, i.e. it should have a
Carath\'{e}odory hyperbolic covering. We study here the plane projective curves
who... | 1995-01-17 | 2014-12-02 | [
"alg-geom",
"math.AG"
] | Gerd Dethloff and Mikhail Zaidenberg |
alg-geom/9501009 | On the Hilbert scheme of curves in higher-dimensional projective space | In this paper we prove that, for any $n\ge 3$, there exist infinitely many
$r\in \N$ and for each of them a smooth, connected curve $C_r$ in $\P^r$ such
that $C_r$ lies on exactly $n$ irreducible components of the Hilbert scheme
$\hilb(\P^r)$. This is proven by reducing the problem to an analogous statement
for the mod... | 1995-01-17 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Barbara Fantechi and Rita Pardini |
alg-geom/9501008 | Quantum cohomology of complete intersections | The quantum cohomology algebra of a projective manifold X is the cohomology
H(X,Q) endowed with a different algebra structure, which takes into account the
geometry of rational curves in X. We show that this algebra takes a remarkably
simple form for complete intersections when the dimension is large enough
w.r.t. the ... | 1995-01-17 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Arnaud Beauville |
alg-geom/9501006 | Boundary behaviour of Hurwitz schemes | Actions of finite groups on stable curves are studied. They appear naturally
at the boundary of a moduli space of smooth curves with group actions. Those
actions which can equivariantly smoothed are characterised. A description of
topological types of those actions in terms of the quotient curve and mappings
from a kin... | 1995-01-16 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Torsten Ekedahl |
alg-geom/9501005 | An improved bound for the degree of smooth surfaces in P4 not of general
type. | This is an addendum to the paper of Braun and Fl{\o}ystad ([BF]) on the bound
for the degree of a smooth surface in $\pfour$ not of general type. Using their
construction and the regularity of curves in $\pthree$, one may lower the bound
a little more. We will prove the following:
Theorem. Let $S$ be a smooth surface... | 1995-01-16 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Michele Cook |
alg-geom/9501004 | ${\bf C}^*$-extensions of tori, higher Chow groups and applications to
incidence equivalence relations for algebraic cycles. | Let X be a smooth projective variety of dimension n. If $p+q=n+1$ then Bloch
has defined a ${\bf G}_m$-biextension E over the product of the Chow groups
$CH^p_0(X)$ and $CH^q_0(X)$ of homologically trivial cycles. We prove that E is
the pullback of the Poincare biextension over the product of intermediate
Jacobians in ... | 1995-01-10 | 2014-10-24 | [
"alg-geom",
"math.AG"
] | Stefan M\"uller-Stach |
alg-geom/9501003 | Moduli of curves with non-abelian level structure | Following Deligne and Mumford we construct a coarse moduli space of smooth
curves with non-abelian level structure, involving higher order commutators. We
prove that its Deligne-Mumford compactification is smooth over an open part of
Spec(${\msy Z}$). | 1995-01-09 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Martin Pikaart and Johan de Jong |
alg-geom/9501002 | Remarks on the Obstructedness of Cones Over Curves of Low Genus | Remarks on the Obstructedness of Cones Over Curves of Low Genus. Reason for
replacement: proof of the main lemma was significantly improved. | 1995-01-06 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Ciro Ciliberto, Angelo Lopez, and Rick Miranda |
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