Cohomology of certain moduli spaces of vector bundles (Q1262912)

Let C be a smooth genus g irreducible projective curve over the complex numbers. Consider the moduli space \(M_ g\) of semi-stable vector bundles on X of rank 2 and trivial determinant. Let \(N_ 0\) be the canonical desingularization of \(M_ g\) (Seshadri). The author provides a simpler proof (than that of Nitsure) that the non-singular model of \(N_ 0\) has torsion free third cohomology group. He also shows that the Betti numbers \(\beta_ i\) satisfy \(\beta_ 3=2 g\) and \(\beta_ 4=\binom{2g}{2}+4\) \((g\geq 4)\).