Hybrid convergence of Kähler-Einstein measures

preprint2020arXivOpen access

Abstract

We compute the hybrid limit (in the sense of Boucksom-Jonsson) of the family of Kähler-Einstein volume forms on a degeneration of canonically polarized manifolds. The limit measure is a weighted sum of Dirac masses at divisorial valuations, determined by the natural algebro-geometric limit of the family. We also make some remarks on the non-archimedean Monge-Ampère operator and hybrid continuity of Kähler-Einstein potentials in this context.

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