Infinitesimal Newton-Okounkov bodies and jet separation

TL;DR

This paper investigates the relationship between Newton-Okounkov bodies, base loci, and jet separation, providing geometric characterizations and insights into Seshadri constants in algebraic geometry.

Contribution

It offers a new convex geometric perspective on base loci and jet separation using infinitesimal Newton-Okounkov bodies, extending surface case results.

Findings

Complete characterizations of augmented and restricted base loci.

Convex geometric description of moving Seshadri constants.

Analysis of simplices in Newton-Okounkov bodies related to jet separation.

Abstract

In this paper we explore the connection between asymptotic base loci and Newton-Okounkov bodies associated to infinitesimal flags. Analogously to the surface case, we obtain complete characterizations of augmented and restricted base loci. Interestingly enough, an integral part of the argument is a study of the relationship between certain simplices contained in Newton-Okoukov bodies and jet separation; our results also lead to a convex geometric description of moving Seshadri constants.