Succesive minima of line bundles

I will discuss a connection between Seshadri constants of line bundles on projective varieties, and successive minima of a 0-symmetric convex body with respect to a lattice. We introduce the successive minima of a line bundle on a projective variety, such that the last minima is the Seshadri constant. We show the analogue of Minkowski's second theorem, namely that the volume of a line bundle is proportional with the product of its successive minima at a very general point. Based on joint work with Atsushi Ito.