Mingxi Wang, Max-Planck Institut, Germany

Moduli space of Higgs bundles over real algebraic curves

Abstract

We study several involutions on the moduli space of Higgs bundles over a real curve: one from the real structure of non-abelian Betti moduli space, one from the real structure of non-abelian Dolbeault moduli space, and one a composition of the previous two. When the real structure of the curve is attached to a Schottky uniformization, there is a correspondence between representations of Schottky group and part of fixed points of our third involution. This correspondence settles a fundamental case of a problem of Faltings.