2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112880We 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 GeometryAlgebraic GeometryDifferential Geometry53C07; 14J60; 32L05text