# Unramified Brauer group of the moduli spaces of \$PGL r{mathbb C}\$-bundles over curves

Let \$X\$ be an irreducible smooth complex projective curve of genus at least two. Let \$N\$ be a connected component of the moduli space of semistable principal \${ m PGL} r{\mathbb C}\$- bundles over \$X\$; it is a normal unirational complex projective variety. We prove that the Brauer group of a desingularization of \$N\$ is trivial.

Author: Indranil Biswas; Amit Hogadi; Yogish I. Holla

Source: https://archive.org/