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Algebraic Geometry papers

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Complements on surfaces
The main result of the paper is a boundedness for n-complements on algebraic surfaces. In addition, applications of this theorem to a classification of log Del Pezzo surfaces and of birational…
V. V. ShokurovMar 28, 2001
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Isolated rational curves on K3-fibered Calabi-Yau threefolds
We study each of the 16 types of complete intersection Calabi-Yau threefolds in projective n-space times the projective line, for various n, and prove existence of isolated rational curves of…
Torsten Ekedahl, Trygve Johnsen, Dag Einar SommervollJan 24, 2001
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Cohomology of complete intersections in toric varieties
This paper explicitly describes Hodge structures of complete intersections of ample hypersurfaces in compact simplicial toric varieties.
Anvar R. MavlyutovDec 20, 2000
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The Gross-Kohnen-Zagier theorem in higher dimensions
The Gross-Kohnen-Zagier theorem describes Heegner points on a modular curve in terms of coefficients of modular forms. We give another proof of this theorem which generalizes to higher dimensions.
Richard E. BorcherdsMay 12, 2000
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Real deformations and complex topology of plane curve singularities
This is the paper as published. The topology of a complex plane curve singularity with real branches is deduced from any real deformation having delta crossings. An example of the computation of the…
Norbert A'CampoApr 3, 2000
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Irreducibility of the moduli space of vector bundles on surfaces and Brill-Noether theory on singular curves
We prove the irreducibility of the moduli space of rank 2 semistable torsion free sheaves (with a generic polarization and any value of c2) on a K3 or a del Pezzo surface. In the case of a K3…
Tomas L. GomezMar 23, 2000
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Degenerations of (1,3) abelian surfaces and Kummer surfaces
We continue our study of the geometry of Nieto's quintic threefold, looking at degenerate surfaces that correspond to certain loci and showing how they arise from a toroidal compactification of a…
K. Hulek, I. Nieto, G. K. SankaranJun 25, 1999
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Heisenberg-invariant Kummer surfaces
We study the geometry of Nieto's quintic threefold (Barth & Nieto, J. Alg. Geom. 3, 1994) and the Kummer and abelian surfaces that correspond to special loci.
K. Hulek, I. Nieto, G. K. SankaranJun 25, 1999
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Zero-pole interpolation for matrix meromorphic functions on a compact Riemann surface, and a matrix Fay trisecant identity
This paper presents a new approach to constructing a meromorphic bundle map between flat vector bundles over a compact Riemann surface having a prescribed Weil divisor (i.e., having prescribed zeros…
Joseph A. Ball, Victor VinnikovFeb 8, 1999
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Involutions on Moduli Spaces and Refinements of the Verlinde Formula
The moduli space M of semi-stable rank 2 bundles with trivial determinant over a complex curve carries involutions naturally associated to 2-torsion points on the Jacobian of the curve. For every…
Jorgen Ellegaard Andersen, Gregor MasbaumDec 14, 1998
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Ladders on Fano varieties
We prove the existence of Fano ladders on weak log Fano varieties of coindex less than 4, as an application of adjunction and nonvanishing.
Florin AmbroDec 1, 1998
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Chern Classes of Bundles over Rational Surfaces
Consider the blow up π: X X of a rational surface X at a point. Let V be a holomorphic bundle over X whose restriction to the exceptional divisor…
Elizabeth GasparimJul 27, 1998
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Hypergeometric functions on reductive groups
The A-hypergeometric system studied by I.M. Gelfand, M.I. Graev, A.V. Zelevinsky and the author, is defined for a set A of characters of an algebraic torus. In this paper we propose a generalization…
M. KapranovApr 6, 1998
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Stringy Hodge numbers of varieties with Gorenstein canonical singularities
We introduce the notion of stringy E-function for an arbitrary normal irreducible algebraic variety X with at worst log-terminal singularities. We prove some basic properties of stringy E-functions…
Victor V. BatyrevMar 16, 1998
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Birational Calabi--Yau n-folds have equal Betti numbers
Let X and Y be two smooth projective n-dimensional algebraic varieties X and Y over C with trivial canonical line bundles. We use methods of p-adic analysis on algebraic varieties over local number…
Victor V. BatyrevMar 16, 1998
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On the index of a vector field at an isolated singularity
We consider manifolds with isolated singularities, i.e., topological spaces which are manifolds (say, C∞--) outside discrete subsets (sets of singular points). For (germs of) manifolds with,…
Wolfgang Ebeling, Sabir M. Gusein-ZadeMar 12, 1998
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Inequalities for semistable families of arithmetic varieties
In this paper, we will consider a generalization of Bogomolov's inequality and Cornalba-Harris-Bost's inequality to semistable families of arithmetic varieties under the idea that geometric…
Shu Kawaguchi, Atsushi MoriwakiMar 3, 1998
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Secondary Kodaira-Spencer classes and nonabelian Dolbeault cohomology
If X is a smooth projective variety moving in a family, we define a secondary Kodaira-Spencer class for nonabelian Dolbeault cohomology Hom(XDol, T) of X with coefficients in the…
Carlos SimpsonJan 6, 1998
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Quantum Hyperplane Section Theorem For Homogeneous Spaces
We formulated a mirror-free approach to the mirror conjecture, namely, quantum hyperplane section conjecture, and proved it in the case of nonnegative complete intersections in homogeneous manifolds.…
Bumsig KimJan 2, 1998
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Comparison of the algebraic and the symplectic Gromov-Witten invariants
We show that the algebraic and the symplectic GW-inivariants of smooth projective varieties are equivalent.
Jun Li, Gang TianJan 1, 1998
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Weak approximation, Brauer and R-equivalence in algebraic groups over arithmetical fields
We prove some new relations between weak approximation and some rational equivalence relations (Brauer and R-equivalence) in algebraic groups over arithmetical fields. By using weak approximation and…
Nguyen Quoc ThangDec 31, 1997
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On the classification of hyperbolic root systems of the rank three. Part II
Here we prove classification results announced in Part I (alg-geom/9711032). We classify maximal hyperbolic root systems of the rank 3 having restricted arithmetic type and a generalized lattice Weyl…
Viacheslav V. NikulinDec 30, 1997
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Descent for Shimura Varieties
We verify that the descent maps provided by Langlands's Conjugacy Conjecture do satisfy the continuity condition necessary for them to be effective. Thus Langlands's conjecture does imply the…
J. S. MilneDec 30, 1997
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Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds
For an arbitrary smooth n-dimensional Fano variety X we introduce the notion of a small toric degeneration. Using small toric degenerations of Fano n-folds X, we propose a general method for…
Victor V. BatyrevDec 30, 1997
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A morphism of intersection homology induced by an algebraic map
Let f:X-->Y be a map of algebraic varieties. Barthel, Brasselet, Fieseler, Gabber and Kaup have shown that there exists a homomorphism of intersection homology groups f*:IH*(Y)-->IH*(X)…
Andrzej WeberDec 30, 1997
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