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Geometry of moduli spaces of Higgs bundles. (English) Zbl 1107.53016

Summary: 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 a natural hyper-Kähler structure.

MSC:

53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
58D27 Moduli problems for differential geometric structures
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