Seshadri constants and the generation of jets

In this paper we explore the connection between Seshadri constants and the generation of jets. It is well known that one way to view Seshadri constants is to consider them as measuring the rate of growth of the number of jets that multiples of a line bundle generate. Here we ask, conversely, what we can say about the number of jets once the Seshadri constant is known. As an application of our results, we prove a characterization of projective space among all Fano varieties in terms of Seshadri constants.