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

Abstract

Let be a geometrically connected smooth projective curve of genus <!-- MATH $g_X \geq 2$ --> over <!-- MATH $\mathbb{R}$ --> . Let be the coarse moduli space of geometrically stable vector bundles over of rank and determinant , where is a real point of the Picard variety <!-- MATH $\underline{\mathrm{Pic}}^d( X)$ --> . If <!-- MATH $g_X = r = 2$ --> , then let be odd. We compute the Brauer group of .