Degeneration of Calabi-Yau metrics and canonical basis
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915289883475968 |
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| author | Li, Yang |
| author_facet | Li, Yang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11087 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Degeneration of Calabi-Yau metrics and canonical basis Li, Yang Differential Geometry Algebraic Geometry 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. |
| title | Degeneration of Calabi-Yau metrics and canonical basis |
| topic | Differential Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2505.11087 |