On volumes and the generic invariance of Fano type varieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916961260142592 |
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| author | Kim, Donghyeon |
| author_facet | Kim, Donghyeon |
| contents | We demonstrate the generic invariance of the Fano type property in cases where the volumes of anti-canonical divisors of Fano type fibers are a constant over a Zariski-dense subset, or the Fano type fibers are dimension $2$. Additionally, paralleling this theorem, we establish a conjecture by Schwede and Smith under the condition that the volumes of anti-canonical divisors remain constant in the reduction mod $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13603 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On volumes and the generic invariance of Fano type varieties Kim, Donghyeon Algebraic Geometry 14E05, 14E30, 14J45, 14G17 We demonstrate the generic invariance of the Fano type property in cases where the volumes of anti-canonical divisors of Fano type fibers are a constant over a Zariski-dense subset, or the Fano type fibers are dimension $2$. Additionally, paralleling this theorem, we establish a conjecture by Schwede and Smith under the condition that the volumes of anti-canonical divisors remain constant in the reduction mod $p$. |
| title | On volumes and the generic invariance of Fano type varieties |
| topic | Algebraic Geometry 14E05, 14E30, 14J45, 14G17 |
| url | https://arxiv.org/abs/2506.13603 |