Birationality of moduli spaces of twisted $\mathrm{U}(p,q)$-Higgs bundles

Abstract

A $\mathrm{U}(p,q)$-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 $\mathrm{U}(p,q)$-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.

29 pages; final version, to appear in Revista Matemática Complutense

Cited by in corpus (3)

• Homotopy Type of Moduli Spaces of G-Higgs Bundles and Reducibility of the Nilpotent Cone
• Quiver Bundles and Wall Crossing for Chains
• Hitchin Pairs for non-compact real Lie groups