Frobenius-Seshadri constants and characterizations of projective space

TL;DR

This paper extends the concept of Frobenius-Seshadri constants to higher orders in positive characteristic and uses them to characterize projective space, paralleling known results in characteristic zero.

Contribution

It introduces higher-order Frobenius-Seshadri constants for ample line bundles in positive characteristic and applies them to characterize projective space.

Findings

Higher-order Frobenius-Seshadri constants are defined for ample line bundles in positive characteristic.

Demailly's criterion for jet separation holds in positive characteristic using these constants.

Characterization of projective space via Seshadri constants in positive characteristic is established.

Abstract

We introduce higher-order variants of the Frobenius-Seshadri constant due to Musta\c{t}\u{a} and Schwede, which are defined for ample line bundles in positive characteristic. These constants are used to show that Demailly's criterion for separation of higher-order jets by adjoint bundles also holds in positive characteristic. As an application, we give a characterization of projective space using Seshadri constants in positive characteristic, which was proved in characteristic zero by Bauer and Szemberg. We also discuss connections with other characterizations of projective space.