M. S. Narasimhan

Abstract:   Let X be a compact Riemann surface of genus g. Denote by  M(r, L) the moduli space of stable vector bundles on X of rank  r and determinant a line bundle L whose degree is coprime to r. It is shown that the number of deformations of the tangent bundle of M(r, L) is equal to the genus  g. Moreover, a  g-parameter family of deformations can be explicitly constructed. The proof involves the use of the Hecke Correspondence and also a study of the Weil map into an intermediary Jacobian of  M(r, L) when  r= 2.