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Algebraic Geometry papers — page 41

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On Quantum Cohomology Rings of Fano Manifolds and a Formula of Vafa and Intriligator
We observe a general structure theorem for quantum cohomology rings, a non-homogeneous version of the usual cohomology ring encoding information about (almost holomorphic) rational curves. An…
Bernd Siebert, Gang TianMar 12, 1994
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Torus embeddings and algebraic intersection complexes, II
In the previous paper, we describe the intersection complexes of a toric variety as a finite complex of graded exterior modules on the associated fan. In this second part, we rewrite it explicitly by…
Masa-Nori IshidaMar 11, 1994
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Torus embeddings and algebraic intersection complexes
We describe the intersection complex of any perversity of a toric variety completely in terms of the associated fan. It is described by a finite complex of finite dimensional graded vector spaces…
Masa-Nori IshidaMar 11, 1994
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Towards a Schubert calculus for maps from a Riemann surface to a Grassmannian
The intuitive notion of the Gromov invariant for maps from a Riemann surface to a Grassmannian is shown to agree with the definition in BDW. Also, an induction on the genus is proved, which…
Aaron BertramMar 10, 1994
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Hyperkaehler Embeddings II
In the first part, Hyperkaehler Embeddings and Holomorphic symplectic Geometry I, we prove the following. Let N be a closed analytic subvariety of a generic deformation of a holomorphically…
Misha VerbitskyMar 6, 1994
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Siegel modular forms generated by invariants of cubic hypersurfaces
We give a geometric derivation of Schottky's equation in genus four for the period matrices of Riemann surfaces among all period matrices. The equation arises naturally from the singularity…
C. McCrory, T. Shifrin, R. VarleyMar 3, 1994
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The versal Deformation of an isolated toric Gorenstein Singularity
Given a lattice polytope Q in Rn, we define an affine scheme M(Q) that reflects the possibilities of splitting Q into a Minkowski sum. On the other hand, Q induces a toric Gorenstein singularity Y,…
Klaus AltmannMar 2, 1994
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Toric Q-Gorenstein Singularities
For an affine, toric Q-Gorenstein variety Y (given by a lattice polytope Q) the vector space T1 of infinitesimal deformations is related to the complexified vector spaces of rational Minkowski…
Klaus AltmannMar 2, 1994
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Intersection Theory on Toric Varieties
The operational Chow cohomology classes of a complete toric variety are identified with certain functions, called Minkowski weights, on the corresponding fan. The natural product of Chow cohomology…
William Fulton, Bernd SturmfelsMar 1, 1994
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Residual Intersections and Some Applications
We give a new residual intersection decomposition for the refined intersection products of Fulton-MacPherson. Our formula refines the celebrated residual intersection formula of Fulton, Kleiman,…
Xian WuMar 1, 1994
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The Deformation Space of Calabi-Yau n-folds with canonical singularities can be obstructed
This paper gives a simple example of a family of Calabi-Yaus of any dimension with canonical singularities of dimension one, whose Kuranishi space is singular. Thus the Bogomolov-Tian-Todorov…
Mark GrossFeb 25, 1994
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Faltings modular height and self-intersection of dualizing sheaf
Let K be a number field, OK the ring of integers of K and X a stable curve over OK of genus g >= 2. In this note, we will prove a strict inequality ( (KX/S)2 / [K : Q] ) > HeightFal(J(XK)),…
Atsushi MoriwakiFeb 17, 1994
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Factorization theorems for the representations of the fundamental groups of quasiprojective varieties and some applications
In this paper, using Gromov-Jost-Korevaar-Schoen technique of harmonic maps to nonpositively curved targets, we study the representations of the fundamental groups of quasiprojective varieties. As an…
Ludmil KatzarkovFeb 16, 1994
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Degree of the generalized Plücker embedding of a Quot scheme and Quantum cohomology
We compute the degree of the generalized Plücker embedding κ of a Quot scheme X over 1. The space X can also be considered as a compactification of the space of algebraic maps of a fixed…
M. S. Ravi, J. Rosenthal, X. WangFeb 15, 1994
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On Polarized Manifolds of Sectional Genus Three
This paper is an attempt for the classification of polarized manifolds of sectional genus g=3 and dimension n≥ 3. As in the case of g≤ 2,which was classified by T.Fujita,we use…
Hironobu IshiharaFeb 14, 1994
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On the Locus of Hodge Classes
Let f: X → S be a family of non singular projective varieties parametrized by a complex algebraic variety S. Fix s ∈ S, an integer p, and a class h ∈ H2p(Xs,) of…
Eduardo Cattani, Pierre Deligne, Aroldo KaplanFeb 10, 1994
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Variation of Geometric Invariant Theory Quotients
Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parametrizing isomorphism classes of…
Igor V. Dolgachev, Yi HuFeb 9, 1994
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Boundedness and K2 for log surfaces
Let ε, C be two positive real numbers, and C ⊂ R be a DCC (descending chain condition) set. Let (X, B = Σ bj Bj) denote a projective surface with an $…
Valery AlexeevFeb 9, 1994
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On surfaces in P4 and 3-folds in P5
This is a survey on the classification of smooth surfaces in P4 and smooth 3-folds in P5. We recall the corresponding results arising from adjunction theory and explain how to construct examples…
Wolfram Decker, Sorin PopescuFeb 8, 1994
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The Tangent Space at a Special Symplectic Instanton Bundle on P2n+1
Mathematical instanton bundles on P3 have their analogues in rank--2n instanton bundles on odd dimensional projective spaces P2n+1. The families of special instanton bundles on these…
Giorgio Ottaviani, Günther TrautmannFeb 7, 1994
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Boundedness theorem for Fano log-threefolds
The main purpose of this article is to prove that the family of all Fano threefolds with log-terminal singularities with bounded index is bounded.
A. BorisovFeb 6, 1994
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The combinatorics of the Verlinde formulas
A residue formula is given for the Verlinde formula, which allows one to calculate its coefficients as a polynomial in the level and connects it to the Riemann-Roch formula on the moduli space of…
Andras SzenesFeb 4, 1994
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Dual Cones and Mirror Symmetry for Generalized Calabi-Yau Manifolds
We introduce a special class of convex rational polyhedral cones which allows to construct generalized Calabi-Yau varieties of dimension (d + 2(r-1)), where r is a positive integer and d is the…
Victor V. Batyrev, Lev A. BorisovFeb 3, 1994
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The theta divisior of the bidegree (2,2) threefold in P2 × P2
Let T be a general bidegree (2,2) divisor in the product of two projective planes. Recently A.Verra proved that the existence of two conic bundle structures (c.b.s.) on T implies a new counterexample…
Atanas IlievFeb 3, 1994
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Diagram Method for 3-Folds and its Application to Kahler Cone and Picard Number of Calabi-Yau 3-Folds, I. with Appendix by Vyacheslav V. Shokurov: "Anticanonical boundedness for curves"
We prove the general diagram method theorem valid for the quite large class of 3-folds with Q-factorial singularities (see Basic Theorem 1.3.2 and also Theorem 2.2.6). This gives the generalization…
Viacheslav V. NikulinJan 31, 1994
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