Geometry of moduli spaces of Higgs bundles

We construct a Petersson-Weil-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 Petersson-Weil 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 Petersson-Weil Kähler form is computed. We also show that, under certain assumptions, a moduli space of Higgs bundles supports of natural hyper-Kähler structure.

2010 Mathematics Subject Classification

Primary 32Gxx. Secondary 14Dxx, 32Jxx.

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Published 1 January 2006