Compactification of moduli of Higgs bundles

TL;DR

This paper constructs a canonical compactification of Hitchin's moduli space of stable Higgs bundles over a Riemann surface, providing a detailed geometric analysis and revalidating previous results on the nilpotent cone.

Contribution

It introduces a new canonical compactification of the moduli space, including a divisor at infinity, and offers a comprehensive study of its geometric properties.

Findings

Constructed a projective compactification of the moduli space.

Analyzed the divisor at infinity and its structure.

Reproved key assertions about the nilpotent cone.

Abstract

In this paper we consider a canonical compactification of Hitchin's moduli space of stable Higgs bundles with fixed determinant of odd degree over a Riemann surface, producing a projective variety by gluing in a divisor at infinity. We give a detailed study of the compactified space, the divisor at infinity and the moduli space itself. In doing so we reprove some assertions of Laumon and Thaddeus on the nilpotent cone.