Brill-Noether theory and Green's conjecture for general curves on simple abelian surfaces

Abstract

In this paper we compute the gonality and the dimension of the Brill-Noether loci W 1 d (C) for curves in a non primitive linear system of a simple abelian surface, adapting vector bundles techniques à la Lazarsfeld originally introduced with K3 surfaces. As a corollary, we obtain general Green's conjecture for curves on abelian surfaces.