Geometry of moduli spaces of Higgs bundles

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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.
To appear in Communications in Analysis and Geometry

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Algebraic Geometry, Differential Geometry, 53C07; 14J60; 32L05

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http://salesiana.dossiersoluciones.com/handle/123456789/112880

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0605589
 http://arxiv.org/abs/math/0605589

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arXiv