Partial Okounkov bodies and Duistermaat--Heckman measures of non-Archimedean metrics

TL;DR

This paper introduces partial Okounkov bodies for Hermitian pseudo-effective line bundles on smooth projective varieties, linking them to singularity invariants and extending Duistermaat--Heckman measures to non-Archimedean metrics.

Contribution

It constructs partial Okounkov bodies as invariants of singularities and generalizes Duistermaat--Heckman measures to finite energy metrics in non-Archimedean geometry.

Findings

Partial Okounkov bodies are universal invariants of singularities.

Generalization of Duistermaat--Heckman measures to non-Archimedean metrics.

Connections between algebraic and non-Archimedean geometry.

Abstract

Let $X$ be a smooth projective variety. We construct partial Okounkov bodies associated to Hermitian pseudo-effective line bundles $(L,\phi)$ on $X$. We show that partial Okounkov bodies are universal invariants of the singularity of $\phi$. As an application, we generalize the theorem of Boucksom--Chen and construct Duistermaat--Heckman measures associated with finite energy metrics on the Berkovich analytification of an ample line bundle.