Universal Chern classes on the moduli of bundles

TL;DR

This paper constructs universal cohomology classes on the moduli space of stable bundles over a curve, extending the theory to cases where the space is not fine due to non-coprimality of rank and degree.

Contribution

It introduces a method to lift Chern classes of the universal bundle to the product of the curve with the moduli space, even when it is not a fine moduli space.

Findings

Chern classes of the universal bundle can be lifted in non-fine cases

The construction applies to moduli spaces where rank and degree are not coprime

Extends the understanding of universal classes on moduli stacks

Abstract

The goal of this paper is to construct universal cohomology classes on the moduli space of stable bundles over a curve when it is not a fine moduli space, i.e. when the rank and degree are not coprime. More precisely, we show that certain Chern classes of the universal bundle on the product of the curve with the moduli stack of bundles lift to the product of the curve with the moduli space of stable bundles.