Seshadri constants for curve classes

TL;DR

This paper extends the concept of Seshadri constants from divisors to movable curve classes on projective varieties, providing new criteria and interpretations for local positivity in algebraic geometry.

Contribution

It introduces a local positivity theory for movable curves, including analogues of classical Seshadri criteria and base locus characterizations, and explores higher codimension cases.

Findings

Developed a Seshadri constant theory for movable curves

Provided criteria for Seshadri ampleness in this context

Connected Seshadri constants to jet separation asymptotics

Abstract

We develop a local positivity theory for movable curves on projective varieties similar to the classical Seshadri constants of nef divisors. We give analogues of the Seshadri ampleness criterion, of a characterization of the augmented base locus of a big and nef divisor, and of the interpretation of Seshadri constants as an asymptotic measure of jet separation. We also study the case of arbitrary codimension.