Rational families of vector bundles on curves

Abstract

We find and describe the irreducible components of the space of rational curves on moduli spaces M of rank 2 stable vector bundles with odd determinant on curves C of genus g [greater than or equal to] 2. We prove that the maximally rationally connected quotient of such a component is either the Jacobian J(C) or a direct sum of two copies of the Jacobian. We show that moduli spaces of rational curves on M are in one-to-one correspondence with moduli of rank 2 vector bundles on the surface P[set]1 x C.