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Algebraic Geometry papers — page 2

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The L2 dbar method, weak Lefschetz theorems, and the topology of Kahler manifolds
A new approach to Nori's weak Lefschetz theorem is described. The new approach, which involves the dbar-method, avoids moving arguments and gives much stronger results. In particular, it is…
T. Napier, M. RamachandranDec 29, 1997
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Reconstruction of a variety from the derived category and groups of autoequivalences
We consider smooth algebraic varieties with ample either canonical or anticanonical sheaf. We prove that such a variety is uniquely determined by its derived category of coherent sheaves. We also…
A. Bondal, D. OrlovDec 24, 1997
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Deformations of canonical singularities
We prove that small deformations of canonical singularities are canonical.
Yujiro KawamataDec 22, 1997
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Symmetric matrices and quantum codes
This paper has been withdrawn since a Gilbert-Varshamov bound for general quantum codes has already appeared in Ekert and Macchiavello, Prys. Rev. Lett. 77, p. 2585, and a Gilbert-Varshamov bound for…
Vladimir D. TonchevDec 22, 1997
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The arithmetic-geometric mean and isogenies for curves of higher genus
Computation of Gauss's arithmetic-geometric mean involves iteration of a simple step, whose algebro-geometric interpretation is the construction of an elliptic curve isogenous to a given one,…
Ron Donagi, Ron LivneDec 21, 1997
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Symplectic cutting of Kaehler manifolds
We obtain estimates on the character of the cohomology of an S1-equivariant holomorphic vector bundle over a Kaehler manifold M in terms of the cohomology of the Lerman symplectic cuts and the…
Maxim BravermanDec 19, 1997
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A canonical lift of Chern-Mather classes
There are several ways to generalize characteristic classes for singular algebraic varieties. The simplest ones to describe are Chern-Mather classes obtained by Nash blow up. They serve as an…
Jean-Paul Brasselet, Andrzej WeberDec 19, 1997
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Poisson structures and birational morphisms associated with bundles on elliptic curves
In this paper we define a Poisson structure on some moduli spaces related to principal G-bundles on elliptic curves, the simplest example being the moduli space of stable pairs: a vector bundle and…
Alexander PolishchukDec 19, 1997
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Analogue of Weil representation for abelian schemes
In this paper we construct a projective action of certain arithmetic group on the derived category of coherent sheaves on an abelian scheme A, which is analogous to Weil representation of the…
Alexander PolishchukDec 19, 1997
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On the cone of curves of an abelian variety
Let X be a smooth projective variety over the complex numbers. One knows by the Cone Theorem that the closed cone of curves of X is rational polyhedral whenever c1(X) is ample. For varieties…
Thomas BauerDec 17, 1997
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Tamagawa numbers of polarized algebraic varieties
Let L = (L, \| · \|v) be an ample metrized invertible sheaf on a smooth quasi-projective algebraic variety V defined over a number field. Denote by N(V, L,B) the number of…
Victor V. Batyrev, Yu. TschinkelDec 17, 1997
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Derived categories of coherent sheaves on abelian varieties and equivalences between them
We study derived categories of coherent sheaves on abelian varieties. We give a criterion for the equivalence of the derived categories on two abelian varieties. We describe the autoequivalence group…
Dmitri OrlovDec 16, 1997
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The Character of the Infinite Wedge Representation
We study the character of the infinite wedge projective representation of the algebra of differential operators on the circle. We prove quasi-modularity of this character and also compute certain…
Spencer Bloch, Andrei OkounkovDec 16, 1997
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Invariance of Plurigenera
The following conjecture on the deformation invariance of plurigenera is proved. For a smooth projective holomorphic family of compact complex manifolds over the open unit 1-disk such that all the…
Yum-Tong SiuDec 15, 1997
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The universal regular quotient of the Chow group of 0-cycles on a singular projective variety
We show the existence of a regular universal quotient as a smooth commutative algebraic group of the Chow group of 0-cycles on a projective reduced variety, and give over the field of complex numbers…
Hélène Esnault, V. Srinivas, Eckart ViehwegDec 15, 1997
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Subadjunction of log canonical divisors II
We extend a subadjunction formula of log canonical divisors as in [K3] to the case when the codimension of the minimal center is arbitrary by using the positivity of the Hodge bundles.
Yujiro KawamataDec 15, 1997
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Eigenvalues of products of unitary matrices and quantum Schubert calculus
We describe the inequalities on the possible eigenvalues of products of unitary matrices in terms of quantum Schubert calculus. Related problems are the existence of flat connections on the punctured…
Sharad Agnihotri, Chris WoodwardDec 14, 1997
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Hyperholomorphic sheaves and new examples of hyperkaehler manifolds
Given a compact hyperkaehler manifold M and a holomorphic bundle B over M, we consider a Hermitian connection ∇ on B which is compatible with all complex structures on M induced by the…
Misha VerbitskyDec 11, 1997
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Mirror Principle I
We propose and study the following Mirror Principle: certain sequences of multiplicative equivariant characteristic classes on Kontsevich's stable map moduli spaces can be computed in terms of…
B. Lian, K. Liu, S. T. YauDec 11, 1997
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Structures du cube et fibres d'intersection
We define the notion of a hypercube structure on a functor between two strictly commutative Picard categories which generalizes the notion of a cube structure on a Gm-torsor over an abelian…
Francois DucrotDec 10, 1997
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Algorithmic Computation of Local Cohomology Modules and the Cohomological Dimension of Algebraic Varieties
In this paper we present algorithms that compute certain local cohomology modules associated to a ring of polynomials containing the rational numbers. In particular we are able to compute the local…
Uli WaltherDec 9, 1997
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Toric varieties and minimal complexes
We translate the equivariant decomposition theorem (in the case of a proper morphism of toric varieties) in to the language of combinatorially defined ``shifted minimal complexes''.
Paul Bressler, Valery LuntsDec 5, 1997
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Homological infiniteness of Torelli groups
We prove that rational homology of the Torelli group of genus g is infinite dimensional, provided g>6. This means that rational homology of the Torelli space of genus g>6 is infinite dimensional. The…
Toshiyuki AkitaDec 3, 1997
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Real Algebraic Threefolds II: Minimal Model Program
This is the second of a series of papers studying real algebraic threefolds using the minimal model program. The main result is the following. Let X be a smooth projective real algebraic 3-fold.…
János KollárDec 2, 1997
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Real Algebraic Threefolds I: Terminal Singularities
This is the first of a series of papers studying real algebraic threefolds using the minimal model program. The main results are outlined in Part II. The present part I. contains the necessary…
János KollárDec 2, 1997
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