The Brauer group of the universal moduli space of vector bundles over smooth curves

TL;DR

This paper calculates the Brauer group of the universal moduli stack of vector bundles over smooth curves, providing explicit descriptions for related moduli spaces, advancing understanding in algebraic geometry.

Contribution

It explicitly determines the Brauer group of the universal moduli stack and the smooth locus of the moduli space of semistable vector bundles for high genus curves.

Findings

Brauer group of the universal moduli stack computed

Explicit description of the Brauer group for the smooth locus

Results applicable to curves of genus at least three and four

Abstract

We compute the Brauer group of the universal moduli stack of vector bundles on (possibly marked) smooth curves of genus at least three over the complex numbers. As consequence, we obtain an explicit description of the Brauer group of the smooth locus of the associated moduli space of semistable vector bundles, when the genus is at least four.