Brill–Noether Theory and Green’s Conjecture for General Curves on Simple Abelian Surfaces

Abstract

Abstract 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 Green’s conjecture for general curves on abelian surfaces. Dedicated to my Grandparents