Geometry of moduli spaces of Higgs bundles
Abstract
We construct a PeterssonWeil type Kähler form on the moduli spaces of Higgs bundles over a compact Kähler manifold. A fiber integral formula for this form is proved, from which it follows that the PeterssonWeil form is the curvature of a certain determinant line bundle, equipped with a Quillen metric, on the moduli space of Higgs bundles over a projective manifold. The curvature of the PeterssonWeil Kähler form is computed. We also show that, under certain assumptions, a moduli space of Higgs bundles supports of natural hyperKähler structure.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2006
 DOI:
 10.48550/arXiv.math/0605589
 arXiv:
 arXiv:math/0605589
 Bibcode:
 2006math......5589B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Differential Geometry;
 53C07;
 14J60;
 32L05
 EPrint:
 To appear in Communications in Analysis and Geometry