Critical k-very ampleness for abelian surfaces

Abstract

Let (S,L) be a polarized abelian surface of Picard rank 1, and let φ be the function which takes each ample line bundle L to the least integer k such that L is k-very ample but not (k+1)-very ample.We use Bridgeland's stability conditions and Fourier- Mukai techniques to give a closed formula for φ(Ln) as a function of n, showing that it is linear in n for n>1. As a by-product, we calculate the walls in the Bridgeland stability space for certain Chern characters.