Moduli of Anti-Invariant Higgs Bundles

TL;DR

This paper establishes the existence and properness of moduli spaces for anti-invariant Higgs bundles, providing new proofs and extending the understanding of their geometric properties.

Contribution

It introduces a new approach to constructing moduli spaces for anti-invariant Higgs bundles using recent existence results, including a non-GIT proof for Higgs bundles.

Findings

Existence of separated good moduli space for semistable anti-invariant Higgs bundles

Proof of properness of the Hitchin system in this setting

Extension of moduli space theory to anti-invariant Higgs bundles

Abstract

We study the moduli of anti-invariant Higgs bundles as introduced by Zelaci. Using recent existence results of Alper, Halpern-Leistner and Heinloth we establish the existence of a separated good moduli space for semistable anti-invariant Higgs bundles. Along the way this produces a non-GIT proof of the existence of a separated good moduli space for semistable Higgs bundles. We also prove the properness of the Hitchin system in this setting.