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

Xia, Mingchen

doi:10.2140/gt.2025.29.1283

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

Mingchen Xia

Geometry & Topology 29 (2025) 1283–1344

DOI: 10.2140/gt.2025.29.1283

Abstract

Let $X$ be a smooth complex projective variety. We construct partial Okounkov bodies associated with Hermitian big line bundles $(L, ϕ)$ on $X$ . We show that partial Okounkov bodies are universal invariants of the singularities of $ϕ$ . As an application, we construct Duistermaat–Heckman measures associated with finite-energy metrics on the Berkovich analytification of an ample line bundle.

Keywords

Okounkov body, pseudoeffective line bundle, plurisubharmonic metric, plurisubharmonic function, convex body

Mathematical Subject Classification

Primary: 14M25, 32U05

References

Publication

Received: 21 March 2022

Revised: 5 March 2024

Accepted: 12 April 2024

Published: 31 May 2025

Proposed: Gang Tian

Seconded: Mark Gross, Leonid Polterovich

Authors

Mingchen Xia
Department of Mathematical Sciences Chalmers Tekniska Högskola Gothenburg Sweden	Institute of Geometry and Physics University of Science and Technology of China (USTC) Shanghai China
http://mingchenxia.github.io/home/

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Volume 29, issue 3 (2025)