From amoebas to pluripotential theory on hybrid analytic spaces

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.

57 pages, expanded version of lectures at the 2024 CIME school `Calabi-Yau varieties'. v2: typos fixed