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Partial Okounkov bodies and Duistermaat--Heckman measures of non-Archimedean metrics (2112.04290v2)

Published 8 Dec 2021 in math.AG, math.CV, and math.DG

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.

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