The meromorphic Hitchin fibration over stable pointed curves: moduli spaces

TL;DR

This paper develops a universal partial compactification of the moduli space of meromorphic Higgs bundles over stable pointed curves, extending the Hitchin fibration and relating fibers to compactified Jacobians, with applications to nilpotent residues.

Contribution

It introduces a new compactification of the moduli space of meromorphic Higgs bundles and extends the Hitchin fibration to this setting, including cases with nilpotent residues.

Findings

Constructed a universal partial compactification of the moduli space.

Extended the Hitchin morphism to the compactified space.

Established a relation between fibers and compactified Jacobians.

Abstract

We construct a universal partial compactification of the relative moduli space of semistable meromorphic Higgs bundles over the stack of stable pointed curves. It parametrizes meromorphic Gieseker Higgs bundles, and is equipped with a flat and proper extension of the usual Hitchin morphism. Over an open subset of the Hitchin base parametrizing allowable nodal spectral covers, we describe the relation of the fibers to compactified Jacobians, thus establishing an analogue of the BNR correspondence. We also construct a version of the moduli space where we require the residues of the meromorphic Higgs bundle to lie in a given set of nilpotent conjugacy classes. In this latter case, we show that there is a flat and proper Hitchin morphism to the flat degeneration of the corresponding family of Hitchin bases constructed in previous physics work.