Brauer group of moduli stack of stable parabolic $\textnormal{PGL}(r)$-bundles over a curve

TL;DR

This paper investigates the Brauer group of the moduli stack of stable parabolic PGL(r)-bundles over a curve, showing it matches that of the smooth locus of the coarse moduli space and computing it for various types.

Contribution

It establishes the equivalence of Brauer groups between the moduli stack and the smooth locus of the coarse moduli space and computes these groups for broader quasi-parabolic configurations.

Findings

Brauer group of the moduli stack equals that of the smooth locus of the coarse moduli space.

Computed the Brauer group for various quasi-parabolic types and weights.

Provided explicit descriptions under certain conditions.

Abstract

Let $k$ be an algebraically closed field of characteristic zero. We prove that the Brauer group of moduli stack of stable parabolic $\textnormal{PGL}(r,k)$-bundles with full flag quasi-parabolic structures at an arbitrary parabolic divisor on a curve $X$ coincides with the Brauer group of the smooth locus of the corresponding coarse moduli space of parabolic $\textnormal{PGL}(r,k)$-bundles. We also compute the Brauer group of the smooth locus of this coarse moduli for more general quasi-parabolic types and weights satisfying certain conditions.