Hodge structure on the cohomology of the moduli space of Higgs bundles
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2001
 arXiv:
 arXiv:math/0112111
 Bibcode:
 2001math.....12111M
 Keywords:

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