Birationality of moduli spaces of twisted U(p, q)-Higgs bundles

Abstract

A U(p, q)-Higgs bundle on a Riemann surface (twisted by a line bundle) consists of a pair of holomorphic vector bundles, together with a pair of (twisted) maps between them. Their moduli spaces depend on a real parameter alpha. In this paper we study wall crossing for the moduli spaces of alpha-polystable twisted U(p, q)-Higgs bundles. Our main result is that the moduli spaces are birational for a certain range of the parameter and we deduce irreducibility results using known results on Higgs bundles. Quiver bundles and the Hitchin-Kobayashi correspondence play an essential role.