Okounkov bodies and Seshadri constants

TL;DR

This paper establishes a connection between Okounkov bodies and Seshadri constants, showing that Okounkov bodies can provide lower bounds for the positivity measures of line bundles.

Contribution

It proves that Okounkov bodies can be used to estimate Seshadri constants, linking convex geometry with line bundle positivity invariants.

Findings

Okounkov bodies give lower bounds for Seshadri constants

Establishes a new method to estimate positivity of line bundles

Bridges convex geometry and algebraic geometry concepts

Abstract

Okounkov bodies, which are closed convex sets defined for big line bundles, have rich information on the line bundles. On the other hand, Seshadri constants are invariants which measure the positivity of line bundles. In this paper, we prove that Okounkov bodies give lower bounds of Seshadri constants.