Cohomology of certain moduli spaces of vector bundles

LetX be a smooth irreducible projective curve of genusg over the field of complex numbers. LetM ₀ be the moduli space of semi-stable vector bundles onX of rank two and trivial determinant. A canonical desingularizationN _o ofM _o has been constructed by Seshadri 17]. In this paper we compute the third and fourth cohomology groups ofN _o. In particular we give a different proof of the theorem due to Nitsure 12], that the third cohomology group ofN _o is torsion-free.