A compactification of the universal moduli space of principal G-bundles

TL;DR

This paper constructs a compactified universal moduli space for semistable principal G-bundles over the moduli space of curves, extending to singular curves with a new stability condition.

Contribution

It introduces a new compactification of the universal moduli space that includes singular principal G-bundles, broadening the scope of moduli space studies.

Findings

Defines a new compactification of the moduli space

Includes moduli of $ ext{delta}$-semistable singular principal G-bundles

Extends the moduli space over singular curves

Abstract

We construct a compactification of the universal moduli space of semistable principal $G$-bundles over $\overline{\textrm{M}}_{g}$, the fibers of which over singular curves are the moduli spaces of $\delta$-semistable singular principal G-bundles.