On the reducibility of moduli spaces of stable 2-bundles over an elliptic surface.
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.
Let be the moduli space of principal -bundles on a curve , and the determinant bundle on . We define an isomorphism of onto the dual of the space of -th order theta functions on the Jacobian of . This isomorphism identifies the rational map defined by the linear system with the map which associates to a quadratic bundle the theta divisor . The two components and of are mapped into the subspaces of even and odd theta functions respectively. Finally we discuss the analogous...
Let be a smooth projective surface, the canonical divisor, a very ample divisor and the moduli space of rank-two vector bundles, -stable with Chern classes and . We prove that, if there exists such that is numerically equivalent to and if is even, greater or equal to , then there is no Poincaré bundle on . Conversely, if there exists such that the number is odd or if is odd, then there exists a Poincaré bundle on .
Let be a closed surface, a compact Lie group, with Lie algebra , and a principal -bundle. In earlier work we have shown that the moduli space of central Yang-Mills connections, with reference to appropriate additional data, is stratified by smooth symplectic manifolds and that the holonomy yields a homeomorphism from onto a certain representation space , in fact a diffeomorphism, with reference to suitable smooth structures and , where denotes the universal central extension of...
Let be a Galois covering of smooth projective curves with Galois group the Weyl group of a simple and simply connected Lie group . For any dominant weight consider the curve . The Kanev correspondence defines an abelian subvariety of the Jacobian of . We compute the type of the polarization of the restriction of the canonical principal polarization of to in some cases. In particular, in the case of the group we obtain families of Prym-Tyurin varieties. The main idea is the use of...
A “relative” -theory group for holomorphic or algebraic vector bundles on a compact or quasiprojective complex manifold is constructed, and Chern-Simons type characteristic classes are defined on this group in the spirit of Nadel. In the projective case, their coincidence with the Abel-Jacobi image of the Chern classes of the bundles is proved. Some applications to families of holomorphic bundles are given and two Riemann-Roch type theorems are proved for these classes.
We determine the type of the zeta functions and the range of the dimensions of the moduli spaces of finite flat models of two-dimensional local Galois representations over finite fields. This gives a generalization of Raynaud’s theorem on the uniqueness of finite flat models in low ramifications.