Moduli space of parahoric Higgs bundles

Abstract

We study parahoric Higgs bundles over a smooth, projective curve. We start out by reviewing the notion of a parahoric group over a local field and associated group schemes constructed by Bruhat and Tits. We continue by reviewing recent criteria to prove the existence of good moduli spaces for an algebraic stack by Alper, Halpern-Leistner and Heinloth. The first result is an application of these criteria to anti-invariant Higgs bundles, which provide a specific example of parahoric Higgs bundles. Lastly, we review work on the moduli of gauged maps by Halpern- Leistner and Herrero and show how this can be used to prove the existence of a moduli space for parahoric Higgs bundles.