The Brauer group of desingularization of moduli spaces of vector bundles over a curve

Abstract

Let C be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic zero. For a fixed line bundle L on C, let MC (r; L) be the coarse moduli space of semistable vector bundles E over C of rank r with ∧rE = L. We show that the Brauer group of any desingularization of MC(r; L) is trivial.