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

Abstract

Let X be a geometrically connected smooth projective curve of genus gX ≥ 2 over R. Let M(r, ξ) be the coarse moduli space of geometrically stable vector bundles E over X of rank r and determinant ξ, where ξ is a real point of the Picard variety Picd(X). If gX = r = 2, then let d be odd. We compute the Brauer group of M(r, ξ).