Brauer group of moduli of stable parabolic $\text{SL}(r,\mathbb{C})$ and $\text{PGL}(r,\mathbb{C})$-connections and Higgs bundles over a curve

TL;DR

This paper computes the Brauer groups of moduli spaces of stable parabolic connections and Higgs bundles on a genus at least 3 Riemann surface, revealing new insights into their algebraic structure.

Contribution

It provides explicit calculations of Brauer groups for these moduli spaces and establishes an equality relating the Brauer group of the moduli stack to its coarse moduli space.

Findings

Brauer groups of moduli spaces are explicitly computed.

An equality between the Brauer group of the moduli stack and the smooth locus of the coarse moduli space is established.

Results deepen understanding of the algebraic structure of moduli spaces over curves.

Abstract

Let $X$ be a compact Riemann surface of genus at least $3$. We compute the Brauer groups of the moduli spaces of stable parabolic $\text{SL}(r,\mathbb{C})$-connections and stable strongly parabolic $\text{SL}(r,\mathbb{C})$-Higgs bundles over $X$. We also establish an equality of the Brauer group of the moduli stack of stable parabolic $\text{PGL}(r,\mathbb{C})$-connections and the smooth locus of its coarse moduli space.