The intersection form on moduli spaces of twisted PGL_n-Higgs bundles vanishes

TL;DR

This paper proves a conjecture that the intersection form on certain moduli spaces of twisted PGL_n-Higgs bundles vanishes when the degree is coprime to n, advancing understanding of their geometric structure.

Contribution

It confirms the vanishing of the intersection form on moduli spaces of stable PGL_n-Higgs bundles when the degree and n are coprime, and establishes irreducibility of moduli spaces of stable chains.

Findings

Intersection form on moduli space vanishes under specified conditions

Moduli spaces of stable chains are irreducible for certain stability parameters

Concludes the conjecture by Hausel and Rodriguez-Villegas

Abstract

Hausel and Rodriguez-Villegas conjectured that the intersection form on the moduli space of stable PGL_n-Higgs bundles on a curve vanishes if the degree is coprime to n. In this note we prove this conjecture. Along the way we show that moduli spaces of stable chains are irreducible for stability parameters larger than the stability condition induced form stability of Higgs bundles.