Non-Archimedean Calabi-Yau Potentials on Certain Affine Varieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908610302312448 |
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| author | Wang, Ying |
| author_facet | Wang, Ying |
| contents | We solve a non-Archimedean Monge-Ampère equation on the Berkovich analytification of a complex log Calabi-Yau pair whose dual complex is a standard simplex, answering a question of Collins-Li and offering a non-Archimedean analog of Ricci-flat metric potentials on complex affine varieties. This work builds on the solution to a complex Monge-Ampère equation obtained by Collins-Li and Collins-Tong-Yau. We also show the suitably rescaled limits of the complex potentials coincide with their non-Archimedean counterparts in some situations, strengthening their connections. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_21677 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Archimedean Calabi-Yau Potentials on Certain Affine Varieties Wang, Ying Algebraic Geometry Differential Geometry 32Q25, 14J32, 14T90, 32P05, 53C23 We solve a non-Archimedean Monge-Ampère equation on the Berkovich analytification of a complex log Calabi-Yau pair whose dual complex is a standard simplex, answering a question of Collins-Li and offering a non-Archimedean analog of Ricci-flat metric potentials on complex affine varieties. This work builds on the solution to a complex Monge-Ampère equation obtained by Collins-Li and Collins-Tong-Yau. We also show the suitably rescaled limits of the complex potentials coincide with their non-Archimedean counterparts in some situations, strengthening their connections. |
| title | Non-Archimedean Calabi-Yau Potentials on Certain Affine Varieties |
| topic | Algebraic Geometry Differential Geometry 32Q25, 14J32, 14T90, 32P05, 53C23 |
| url | https://arxiv.org/abs/2510.21677 |