Irreducibility of moduli of semi-stable chains and applications to U(P, q)-Higgs bundles

Abstract

We give necessary and sufficient conditions for moduli spaces of semi-stable chains on a curve to be irreducible and non-empty. This gives information on the irreducible components of the nilpotent cone of GL n -Higgs bundles and the irreducible components of moduli of systems of Hodge bundles on curves. As we do not impose coprimality restrictions, we can apply this to prove connectedness for moduli spaces of U(p, q)-Higgs bundles. (c) Oxford University Press 2018.