Brauer group of moduli stacks of parabolic principal bundles over a curve

Abstract

We prove that the Brauer group of the moduli stack of parabolic stable principal $\text{PGL}(r,\mathbb{C})$-bundles on a curve $X$, for a generic system of weights along an arbitrary parabolic divisor, coincides with the Brauer group of the smooth locus of the corresponding coarse moduli space of parabolic stable principal $\text{PGL}(r,\mathbb{C})$-bundles. We also show that for any simple and simply connected complex linear algebraic group $G$, the analytic and algebraic Brauer groups of the moduli stack of quasi-parabolic principal $G$-bundles on $X$ vanish.