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Let $X$ be an irreducible smooth complex projective curve of genus at leasttwo. Let $N$ be a connected component of the moduli space of semistableprincipal ${\rm PGL}_r({\mathbb C})$- bundles over $X$; it is a normalunirational complex projective variety. We prove that the Brauer group of adesingularization of $N$ is trivial.

Unramified Brauer group of the moduli spaces of $PGL_r({\mathbb C})$-bundles over curves