Hodge cycles on some moduli spaces

Details Hodge cycles on some moduli spaces Hodge cycles on some moduli spaces

2001-02-08

arxiv.org/abs/math/0102070v5

Mathematics

Algebraic Geometry

28 pages latex; This is a major revision with new material on generalized Hodge conjecture and moduli of bundles over abelian

Scientific paper

The goal is to verify the Hodge conjecture (and some related conjectures) for certain moduli spaces. It is shown that the (generalized) Hodge conjecture holds for the projective moduli spaces of vector bundles over an abelian or K3 surface or a curve if it holds for all powers of the surface or curve. In the latter case, the curve can be replaced by its Jacobian. As a consequence the generalized Hodge conjecture holds for these moduli spaces when the curve is very general. A similar result is proved for the Hilbert schemes of points over an arbitrary surface.

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