Infinitesimal Newton–Okounkov bodies and jet separation

Abstract

In this article 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.