A degeneration of moduli of Hitchin pairs

TL;DR

This paper constructs a degeneration of the moduli space of Hitchin pairs on curves degenerating to a nodal curve, providing a new compactification of the Picard variety with proper Hitchin map.

Contribution

It introduces a novel degeneration model for Hitchin moduli spaces on singular curves, extending prior models for classical moduli spaces.

Findings

The relative Hitchin map is proper.

The general fiber offers a new compactification of the Picard variety.

The construction parallels Gieseker and Nagaraj-Seshadri models.

Abstract

We construct a degeneration of the moduli space of Hitchin pairs on smooth projective curves when the curve degenerates to an irreducible curve with a single node. The degeneration constructed here is analogous to the models constructed by Gieseker and Nagaraj-Seshadri for the case of the usual moduli spaces (i.e when the Higgs structure is trivial). There is an canonical relative Hitchin map which is shown to be proper and the general fibre of the relative Hitchin map provides a new compactification of the Picard variety of smooth curves with normal crossing singularities.