Seshadri constants and the generation of jets

TL;DR

This paper investigates the relationship between Seshadri constants and jet generation, providing new insights into how these constants influence the number of jets a line bundle can generate, with applications to characterizing projective space among Fano varieties.

Contribution

It establishes a novel connection between Seshadri constants and jet generation, and characterizes projective space among Fano varieties using these constants.

Findings

Seshadri constants determine the growth rate of generated jets.

Characterization of projective space via Seshadri constants among Fano varieties.

New bounds relating Seshadri constants to jet generation.

Abstract

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.