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

Xia, Mingchen¹

¹Department of Mathematical Sciences, Chalmers Tekniska Högskola, Gothenburg, Sweden, Institute of Geometry and Physics, University of Science and Technology of China (USTC), Shanghai, China

Geometry & topology, Tome 29 (2025) no. 3, pp. 1283-1344

Résumé

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.

Détail

DOI : 10.2140/gt.2025.29.1283

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

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