Intermediate Jacobians and Hodge Structures of Moduli Spaces

Details Intermediate Jacobians and Hodge Structures of Moduli Spaces Intermediate Jacobians and Hodge Structures of Moduli Spaces

1999-08-09

arxiv.org/abs/math/9908037v2

Proc. Indian Acad. Sci. Math. Sci. 110 (2000)

Mathematics

Algebraic Geometry

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 a

Scientific paper

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.

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