Buser-Sarnak invariant and projective normality of abelian varieties

Abstract

We show that a general $n$-dimensional polarized abelian variety $(A,L)$ of a given polarization type and satisfying $h^0(A,L)\ge \frac{8^n}{2}\cdot \frac{n^n}{n!}$ is projectively normal. In the process, we also obtain a sharp lower bound for the volume of a purely one-dimensional complex analytic subvariety in a geodesic tubular neighborhood of a subtorus of a compact complex torus.

to appear in the Proceedings of CDG2009 (Hannover)