Abstract
Let (S, L) be a polarized abelian surface of Picard rank 1, and let phi 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 phi(L-n) as a function of n, showing that it is linear inn for n > 1. As a by-product, we calculate the walls in the Bridgeland stability space for certain Chern characters.