DIMENSION OF THE SPACE OF SECTIONS OF THE GENERALIZED THETA DIVISOR

Let M be the moduli space of rank 2 stable vector bundles of fixed determinant of odd degree on a curve C of genus greater-than-or-equal-to 2. The Picard group of M is Z. Let O(THETA) be its ample generator. We prove that The dimension of H-0(M, O(THETA)) is the expected dimension : the number of odd theta-characteristics on C. Using some of Beauville's results, this give an explicit basis of this space.