Intermediate Jacobians and Hodge Structures of Moduli Spaces
Abstract
Let SU_X(n,L) be the moduli space of rank n semistable vector bundles with fixed determinant L on a smooth projective genus g>1 curve X. Let SU_X^s(n,L) denote the open subset parameterizing stable bundles. We show that for small i, the mixed Hodge structure on H^i(SU_X^s(n, L), Q) is independent of the degree of L, and hence pure of weight i. Moreover any simple factors is, up to Tate twisting, isomorphic to a summand of a tensor power of H^1(X,Q). A more precise statement for i = 3, yields a Torelli theorem complementing earlier work of several authors. This is a replacement of our preprint Intermediate Jacobians of Moduli spaces which contained a gap.
Cite
@article{arxiv.math/9908037,
title = {Intermediate Jacobians and Hodge Structures of Moduli Spaces},
author = {Donu Arapura and Pramathanath Sastry},
journal= {arXiv preprint arXiv:math/9908037},
year = {2007}
}
Comments
It was brought to our attention, by H. Esnault, that the hyperplane H in our thm 6.1.1 needs to be general. Further comments are contained in the text