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arXiv · 2505.11087

Degeneration of Calabi-Yau metrics and canonical basis

Yang Li
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Abstract

For polarised degenerations of Calabi-Yau manifolds whose essential skeleton has dimension $1\leq m\leq n$, we show that the $C^0$ 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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Yang Li. 2025-05-16. Degeneration of Calabi-Yau metrics and canonical basis. https://arxiv.org/abs/2505.11087

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