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Geometry of moduli spaces of Higgs bundles

Indranil Biswas·Georg Schumacher
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Abstract

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.

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Indranil Biswas, Georg Schumacher. 2006-05-22. Geometry of moduli spaces of Higgs bundles. https://arxiv.org/abs/math/0605589

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