Brauer group of moduli of Higgs bundles and connections

TL;DR

This paper computes the Brauer group of the smooth moduli spaces of Higgs bundles and connections on a compact Riemann surface for a semisimple algebraic group, advancing understanding of their geometric properties.

Contribution

It provides the first explicit calculation of the Brauer group for these moduli spaces, linking algebraic geometry and gauge theory.

Findings

Brauer group of Higgs bundle moduli space determined

Brauer group of connection moduli space determined

Results enhance understanding of geometric structures of moduli spaces

Abstract

Given a compact Riemann surface $X$ and a semisimple affine algebraic group $G$ defined over $\mathbb C$, there are moduli spaces of Higgs bundles and of connections associated to $(X,\, G)$. We compute the Brauer group of the smooth locus of these varieties.