Mathematics

I will give a description of moduli spaces of vector bundles with additional structures (for example flat connections and Higgs bundles) on an abelian variety. The main result is that, under some assumption on the Hilbert polynomial, these are isomorphic to the symmetric product of the moduli space of rank one objects. The main tool is a generalization of the Fourier-Mukai correspondence due to Laumont and Polishuck-Rothstein. Moreover, we find a correspondence between the Hilbert scheme of points of the moduli space of rank one objects and the moduli space of a rigidification of the original moduli problem.

This is a joint work with E. Franco