Valuative independence for Calabi--Yau varieties
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914521068601344 |
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| author | Blum, Harold Liu, Yuchen |
| author_facet | Blum, Harold Liu, Yuchen |
| contents | We construct valuatively independent bases for the space of sections of an ample line bundle on a log Calabi--Yau pair over a discretely valued field and the space of regular functions on an affine CY pair with maximal boundary. While the bases are not in general unique, they induce canonical functions on the respective skeletons and are expected to agree with tropicalizations of theta functions when they exist. The proof uses techniques from the study of higher rank degenerations in K-stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27890 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Valuative independence for Calabi--Yau varieties Blum, Harold Liu, Yuchen Algebraic Geometry Differential Geometry 14J32, 14E30, 14T05 We construct valuatively independent bases for the space of sections of an ample line bundle on a log Calabi--Yau pair over a discretely valued field and the space of regular functions on an affine CY pair with maximal boundary. While the bases are not in general unique, they induce canonical functions on the respective skeletons and are expected to agree with tropicalizations of theta functions when they exist. The proof uses techniques from the study of higher rank degenerations in K-stability. |
| title | Valuative independence for Calabi--Yau varieties |
| topic | Algebraic Geometry Differential Geometry 14J32, 14E30, 14T05 |
| url | https://arxiv.org/abs/2604.27890 |