Abstract
Let X X be a complete nonsingular algebraic curve over C {\mathbf {C}} and L L a line bundle of degree 1 over X X . It is well known that the isomorphism classes of stable bundles of rank 2 and determinant L L over X X form a nonsingular projective variety S ( X ) S(X) . The Betti numbers of S ( X ) S(X) are also known. In this paper we define certain distinguished cohomology classes of S ( X ) S(X) and prove that these classes generate the rational cohomology ring. We also obtain expressions for the Chern character and Pontrjagin classes of S ( X ) S(X) in terms of these generators.