# Irreducibility of moduli of semistable Chains and applications to U(p,q)-Higgs bundles

## TL;DR

This paper establishes criteria for the irreducibility of moduli spaces of semistable chains on curves, with applications to the structure of Higgs bundle moduli spaces and U(p,q)-Higgs bundles.

## Contribution

It provides necessary and sufficient conditions for irreducibility of these moduli spaces without coprimality restrictions, enabling new connectedness results.

## Key findings

- Criteria for irreducibility of moduli spaces of semistable chains
- Application to irreducible components of nilpotent cones of Higgs bundles
- Proof of connectedness for moduli of U(p,q)-Higgs bundles

## Abstract

We give necessary and sufficient conditions for moduli spaces of semistable 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.