Hodge structure on the cohomology of the moduli space of Higgs bundles

Details Hodge structure on the cohomology of the moduli space of Higgs bundles Hodge structure on the cohomology of the moduli space of Higgs bundles

2001-12-12

arxiv.org/abs/math/0112111v2

Mathematics

Algebraic Geometry

7 pages. The only change is the addition of a reference to the proof of the generation theorem for general rank by E. Markman

Scientific paper

We study the moduli space of Higgs bundles on a compact Riemann surface. It was shown by Thaddeus and Hausel (in rank 2) and Markman (in general rank) that the rational cohomology ring of this space is generated by universal classes. In this paper, we use their results to compute the Hodge structure on the cohomology of this moduli space. We show that the natural Hodge structure on H^k is pure of weight k.

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