Weil-Petersson Currents for Holomorphic Vector Bundles and applications

We show that the Weil-Petersson form on the moduli space of stable vector bundles on a projective variety extends to a compactification of the moduli space as a positive current with at most analytic singularities. A certain determinant line bundle embeds the moduli space into a projective space. Similar results hold for vector bundles on orbifolds of Hodge type.