Constructing Indecomposable Motivic Cohomology Classes on Algebraic SurfacesWe describe a method to construct indecomposable classes in Bloch's higher Chow group CH2(X,1) on algebraic surfaces over the complex numbers via transcendental methods and apply it to obtain…Stefan Müller-Stach·Nov 2, 1995SaveLearn
Instantons and affine Lie algebrasVarious constructions of the affine Lie algebra action on the homology group of moduli spaces of instantons on 4-manifolds are discussed. The analogy between the local-global principle and the role…Hiraku Nakajima·Nov 2, 1995SaveLearn
Mixed Hodge structures of configuration spacesThe symmetric group Sn 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 Sn on the de Rham…Ezra Getzler·Nov 1, 1995SaveLearn
GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau HypersurfacesWe 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…S. Hosono, B. H. Lian, S. -T. Yau·Nov 1, 1995SaveLearn
Explicit Enumerative Geometry for the Real Grassmannian of Lines in Projective SpaceWe 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…Frank Sottile·Oct 31, 1995SaveLearn
Rational curves of degree at most 9 on a general quintic threefoldWe prove the following form of the Clemens conjecture in low degree. Let d9, and let F be a general quintic threefold in 4. Then (1)~the Hilbert scheme of rational, smooth and…Trygve Johnsen, Steven L. Kleiman·Oct 30, 1995SaveLearn
Infinite Grassmannians and Moduli Spaces of G-bundlesThis 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)Shrawan Kumar·Oct 30, 1995SaveLearn
Manin's conjecture for toric varietiesWe 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…Victor V. Batyrev, Yuri Tschinkel·Oct 26, 1995SaveLearn
Second N=1 Superanalog of Complex StructureWe 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…Steven Duplij·Oct 19, 1995SaveLearn
Lectures on Seiberg-Witten InvariantsThese 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.Selman Akbulut·Oct 15, 1995SaveLearn
Quantum cohomology of projective bundles over nResults 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…Zhenbo Qin, Yongbin Ruan·Oct 14, 1995SaveLearn
Parabolic Higgs bundles and Teichmüller spaces for punctured surfacesIn 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…Indranil Biswas, Pablo Gastesi, Suresh Govindarajan·Oct 14, 1995SaveLearn
Nilpotent groups and universal coverings of smooth projective varietiesIn this paper we prove that the universal cover of a smooth projective variety with nilpotent fundamental group is holomorphically convex.Ludmil Katzarkov·Oct 13, 1995SaveLearn
K3 surfaces, Lorentzian Kac--Moody algebras and Mirror SymmetryWe 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…Valeri A. Gritsenko, Viacheslav V. Nikulin·Oct 8, 1995SaveLearn
Smooth Formal Embeddings and the Residue ComplexLet π: X -> S be a finite type morphism of noetherian schemes. A smooth formal embedding of X (over S) is a bijective closed immersion X -> X, where X is a noetherian formal scheme,…Amnon Yekutieli·Oct 5, 1995SaveLearn
Some Remarks on Beilinson AdelesThis 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…Amnon Yekutieli·Oct 5, 1995SaveLearn
On the Brill-Noether Problem for Vector BundlesOn 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…Georgios Daskalopoulos, Richard Wentworth·Oct 5, 1995SaveLearn
On Fujita's freeness conjecture for 3-folds and 4-foldsThe result on 3-fold is now optimal by the result of Ein-Lazarsfeld and Helmke.Yujiro Kawamata·Oct 3, 1995SaveLearn
Finiteness Theorem for Sp(4,Z)We consider Siegel upper half space of rank two H2 and different subgroups H⊂eq Sp(4,Z) of finite index. The purpose of this paper is to prove that the field of rational…Lev A. Borisov·Oct 2, 1995SaveLearn
The weight-two Hodge structure of moduli spaces of sheaves on a K3 surfaceWe 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…Kieran G. O'Grady·Oct 2, 1995SaveLearn
Bogomolov conjecture for curves of genus 2 over function fieldsIn this note, we will show that Bogomolov conjecture holds for a non-isotrivial curve of genus 2 over a function field.Atsushi Moriwaki·Oct 1, 1995SaveLearn
Mirror duality and string-theoretic Hodge numbersWe 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…Victor V. Batyrev, Lev A. Borisov·Oct 1, 1995SaveLearn
Obstruction bundles, semiregularity, and Seiberg-Witten invariantsWe compare the deformation theory and the analytic structure of the Seiberg-Witten moduli spaces of a Kähler surface to the corresponding components of the Hilbert scheme, and show that they are…Robert Friedman, John W. Morgan·Sep 29, 1995SaveLearn
The Toda hierarchy and the KdV hierarchyThe 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…D. Gieseker·Sep 26, 1995SaveLearn
Gorenstein algebras, symmetric matrices, self-linked ideals, and symbolic powersInspired 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…Steven Kleiman, Bernd Ulrich·Sep 10, 1995SaveLearn