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On the strange duality conjecture for abelian surfaces

Alina Marian, Dragos Oprea (2014)

Journal of the European Mathematical Society

We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of equal ranks and ber degree 1. The birational type of the moduli space of sheaves is also investigated. Generalizations to arbitrary product elliptic surfaces are given.

Orbifolds, special varieties and classification theory

Frédéric Campana (2004)

Annales de l’institut Fourier

This article gives a description, by means of functorial intrinsic fibrations, of the geometric structure (and conjecturally also of the Kobayashi pseudometric, as well as of the arithmetic in the projective case) of compact Kähler manifolds. We first define special manifolds as being the compact Kähler manifolds with no meromorphic map onto an orbifold of general type, the orbifold structure on the base being given by the divisor of multiple fibres. We next show that rationally connected Kähler...

Orbifolds, special varieties and classification theory: an appendix

Frédéric Campana (2004)

Annales de l’institut Fourier

For any compact Kähler manifold X and for any equivalence relation generated by a symmetric binary relation with compact analytic graph in X × X , the existence of a meromorphic quotient is known from Inv. Math. 63 (1981). We give here a simplified and detailed proof of the existence of such quotients, following the approach of that paper. These quotients are used in one of the two constructions of the core of X given in the previous paper of this fascicule, as well as in many other questions.

Orthogonal bundles on curves and theta functions

Arnaud Beauville (2006)

Annales de l’institut Fourier

Let be the moduli space of principal SO r -bundles on a curve C , and the determinant bundle on . We define an isomorphism of H 0 ( , ) onto the dual of the space of r -th order theta functions on the Jacobian of C . This isomorphism identifies the rational map | | * defined by the linear system | | with the map | r Θ | which associates to a quadratic bundle ( E , q ) the theta divisor Θ E . The two components + and - of are mapped into the subspaces of even and odd theta functions respectively. Finally we discuss the analogous...

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