American Journal of Mathematics

We show that on a complex abelian variety of dimension two or greater the Seshadri constant of an ample line bundle is at least one. Moreover, the Seshadri constant is equal to one if and only if the polarized abelian variety splits as a product of a principally polarized elliptic curve and a polarized abelian subvariety of codimension one. We also examine the case when the Seshadri constant is not one and obtain lower bounds when the dimension of the abelian variety is small.