Universal moduli spaces of vector bundles and the log-minimal model program on the moduli of curves

TL;DR

This paper constructs a universal moduli space of slope semi-stable sheaves that compactifies the space of vector bundles over pseudo-stable curves, advancing the understanding of moduli spaces in the context of the log minimal model program.

Contribution

It introduces a universal moduli space of slope semi-stable sheaves that extends the moduli space of vector bundles over pseudo-stable curves, linking to the Hassett-Keel program.

Findings

Constructed a universal moduli space of slope semi-stable sheaves.

Compactified the moduli space of vector bundles over pseudo-stable curves.

Connected to the log minimal model program for moduli of curves.

Abstract

Recent work on the log minimal model program for the moduli space of curves, as well as past results of Caporaso, Pandharipande, and Simpson motivate an investigation of compactifications of the universal moduli space of slope semi-stable vector bundles over moduli spaces of curves arising in the Hassett-Keel program. Our main result is the construction of a universal moduli space of slope semi-stable sheaves which compactifies the moduli space of vector bundles over the moduli space of pseudo-stable curves.