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Algebraic Geometry papers — page 18

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Genus one enumerative invariants in Pn with fixed j invariant
We prove recursive formulas for τd, the number of degree d elliptic curves with fixed j-invariant in Pn. We use analysis to relate the classical invariant τd to the genus one perturbed…
Eleny IonelAug 26, 1996
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Hodge and Tate conjectures for hypergeometric sheaves
A constructible sheaf corresponding to Gel'fand Zelevinski hypergeometric functions on a torus is called hypergeometric sheaf. We consider Hodge and Tate conjectrue for hypergeomtric sheaves.…
Tomohide TerasomaAug 25, 1996
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Intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a Riemann surface
We prove formulas (found by Witten in 1992 using physical methods) for intersection pairings in the cohomology of the moduli space M(n,d) of stable holomorphic vector bundles of rank n and degree d…
Lisa C. Jeffrey, Frances C. KirwanAug 23, 1996
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Holomorphic bundles on O(-k) are algebraic
We show that holomorphic bundles on O(-k) for k > 0 are algebraic. We also show holomorphic bundles on O(-1) are trivial outside the zero section.
Elizabeth GasparimAug 23, 1996
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Algebraic Cuts
Let X be a projective variety with a torus action, which for simplicity we assume to have dimension 1. If X is a smooth complex variety, then the geometric invariant theory quotient X//G can be…
Dan Edidin, William GrahamAug 23, 1996
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The intersection form in the cohomology of the moduli space of genus 0 n-pointed curves H*(M0,n) and the explicit Künneth formula in quantum cohomology
We prove a general formula for the intersection form of two arbitrary monomials in boundary divisors. Furthermore we present a tree basis of the cohomology of M0,n. With the help of…
Ralph KaufmannAug 22, 1996
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Counting plane curves of any genus
We obtain a recursive formula answering the following question: How many irreducible, plane curves of degree d and (geometric) genus g pass through 3d-1+g general points in the plane? The formula is…
Lucia Caporaso, Joe HarrisAug 22, 1996
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Parameter spaces for curves on surfaces and enumeration of rational curves
We answer some enumerative questions about irreducible rational curves on Hirzebruch surfaces, by combining an idea of Kontsevich with the study of the geometry of certain natural parameter spaces.…
Lucia Caporaso, Joe HarrisAug 22, 1996
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Enumerating curves on rational surfaces: the rational fibration method
A new, simple method to approach enumerative questions about rational curves on rational surfaces is described. Applications include a short proof of Kontsevich's formula for plane curves and a…
Lucia Caporaso, Joe HarrisAug 22, 1996
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Rank Two Bundles on Algebraic Curves and Decoding of Goppa Codes
We study a connection between two topics: Decoding of Goppa codes arising from an algebraic curve, and rank two extensions of certain line bundles on the curve.
Trygve JohnsenAug 21, 1996
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Some adjunction-theoretic properties of codimension two nonsingular subvarieties of quadrics
We make precise the structure of the first two reduction morphisms associated with codimension two nonsingular subvarieties of quadrics n, n≥ 5. We give a coarse classification of the same…
Mark Andrea A. de CataldoAug 21, 1996
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Codimension two nonsingular subvarieties of quadrics: scrolls and classification in degree d≤ 10
Let X be a codimension two nonsingular subvariety of a nonsingular quadric n of dimension n≥ 5. We classify such subvarieties when they are scrolls. We also classify them when the degree…
Mark Andrea A. de CataldoAug 21, 1996
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A finiteness theorem for low-codimensional nonsingular subvarieties of quadrics
We prove that there are only finitely many families of codimension two nonsingular subvarieties of quadrics n which are not of general type, for n=5 and n≥ 7. We prove a similar…
Mark Andrea A. de CataldoAug 21, 1996
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The genus of curves on the three dimensional quadric
By means of an ad hoc modification of the so-called ``Castelnuovo-Harris analysis" we derive an upper bound for the genus of integral curves on the three dimensional nonsingular quadric…
Mark Andrea A. de CataldoAug 21, 1996
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On the Thomae formula for ZN curves
We shall give an elementary and rigorous proof of the Thomae formula for ZN curves which was discovered by Bershadsky and Radul. Instead of using the determinant of the Laplacian we use the…
Atsushi NakayashikiAug 20, 1996
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Balanced Varieties
After the work of Bloch and Srinivas on correspondences and algebraic cycles we begin the study of a birational class of algebraic varieties determined by the property that a multiple of the diagonal…
L. Barbieri-VialeAug 20, 1996
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Complete intersections and rational equivalence
Two cycles on a projective variety over an algebraically closed field are shown to be rationally equivalent if and only if their difference equals a difference of complete intersections of a certain…
R. BarlowAug 20, 1996
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Compactified jacobians
Let J be the jacobian of a reduced projective curve C with nodes only. 1) We give a simple and natural definition for its many compactifications and show the connection with various other definitions…
Valery AlexeevAug 17, 1996
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On Mumford's construction of degenerating abelian varieties
We prove that a 1-dimnl family of abelian varieties with an ample sheaf defining principal polarization can be canonically compactified (after a finite base change) to a projective family with an…
Valery Alexeev, Iku NakamuraAug 17, 1996
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Log canonical singularities and complete moduli of stable pairs
1) Assuming log Minimal Model Conjecture, we give a construction of a complete moduli space of stable log pairs of arbitrary dimension generalizing directly the space Mg,n of pointed stable…
Valery AlexeevAug 17, 1996
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Notes on stable maps and quantum cohomology
These are notes from a jointly taught class at the University of Chicago and lectures by the first author in Santa Cruz. Topics covered include: construction of moduli spaces of stable maps,…
W. Fulton, R. PandharipandeAug 15, 1996
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Lower Bounds for diophantine Approximation
We introduce a subexponential algorithm for geometric solving of multivariate polynomial equation systems whose bit complexity depends mainly on intrinsic geometric invariants of the solution set.…
M. Giusti, J. Heintz, K. Hägele et al.Aug 13, 1996
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Residues in intersection homology and Lp-cohomology
Suppose Mn+1 is a complex manifold and K is a hypersurface with isolated singularities. Let ω be a holomorphic form on M K with the first order pole on K. The Leray residue of such…
Andrzej WeberAug 10, 1996
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Vanishing Theorems and Syzygies for K3 Surfaces and Fano Varieties
In this article we prove some strong vanishing theorems on K3 surfaces. As an aplication of them, we obtain higher syzygy results for K3 surfaces and Fano varieties.
F. J. Gallego, B. P. PurnaprajnaAug 7, 1996
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The Geometry Underlying Mirror Symmetry
The recent result of Strominger, Yau and Zaslow relating mirror symmetry to the quantum field theory notion of T-duality is reinterpreted as providing a way of geometrically characterizing which…
David R. MorrisonAug 5, 1996
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