Cohomology of certain moduli spaces of vector bundles

Abstract

Let X be a smooth irreducible projective curve of genusg over the field of complex numbers. Let M₀ be the moduli space of semi-stable vector bundles onX of rank two and trivial determinant. A canonical desingularization N_o of M_o has been constructed by Seshadri [17]. In this paper we compute the third and fourth cohomology groups of N_o. In particular we give a different proof of the theorem due to Nitsure [12], that the third cohomology group of N_o is torsion-free.