Line Bundles Over Families of (SUPER) Riemann Surfaces. I: The   Non-Graded Case
  A first step towards a systematic theory of relative line bundles over SUSY-curves is presented. In this paper we deal with the case of relative line bundles over families of ordinary Riemann surfaces. Generalizations of the Gauss-Bonnet theorem and of the flatness theorem for line bundles are discussed. 
U. Bruzzo and J.A. Dominguez Perez