Degeneration of Calabi-Yau metrics and canonical basis

2025/05/16 by Li, Yang · 1 citation
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.11087

Abstract

For polarised degenerations of Calabi-Yau manifolds whose essential skeleton has dimension 1≤ m≤ n, we show that the C⁰ potential theoretic limit of the Calabi-Yau metrics agrees with the non-archimedean Calabi-Yau metric on the Berkovich analytification. Moreover, this limit data can be encoded into the unique minimiser of the Kontorovich functional of an optimal transport problem, under some algebro-geometric assumptions on the existence of a canonical basis of sections for tensor powers of the polarisation line bundle.

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