A Frobenius variant of Seshadri constants

TL;DR

This paper introduces a Frobenius-based variant of Seshadri constants in positive characteristic and demonstrates its implications for the global generation and very ampleness of adjoint line bundles, extending known criteria to positive characteristic.

Contribution

It defines a new Frobenius-based Seshadri constant and proves its bounds imply global generation and very ampleness in positive characteristic, extending classical results.

Findings

Lower bounds imply global generation

Lower bounds imply very ampleness

Criteria extend to positive characteristic

Abstract

We define and study a version of Seshadri constant for ample line bundles in positive characteristic. We prove that lower bounds for this constant imply the global generation or very ampleness of the corresponding adjoint line bundle. As a consequence, we deduce that the criterion for global generation and very ampleness of adjoint line bundles in terms of usual Seshadri constants holds also in positive characteristic.