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arXiv · 2510.10239

From amoebas to pluripotential theory on hybrid analytic spaces

Sebastien Boucksom
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Abstract

These lecture notes are an introduction to the use of non-Archimedean geometry in the study of meromorphic degenerations of complex algebraic varieties. They provide a self-contained discussion of hybrid spaces, which fill in one-parameter degenerations with the associated non-Archimedean Berkovich space as a central fiber. The main focus is on the interplay between complex and non-Archimedean pluripotential theory, and on the relation between convergence of psh metrics and the associated Monge-Ampere measures in the hybrid space, following work of the author with M.Jonsson, and recent breakthrough work by Y.Li.

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Sebastien Boucksom. 2025-10-11. From amoebas to pluripotential theory on hybrid analytic spaces. https://arxiv.org/abs/2510.10239

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