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

Journal article, 2025

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.