Variation of cones of divisors in a family of varieties -- Fano type case
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914275953475584 |
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| author | Choi, Sung Rak Li, Zhan Zhou, Chuyu |
| author_facet | Choi, Sung Rak Li, Zhan Zhou, Chuyu |
| contents | We investigate the relationship between the Fano type property on fibers over a Zariski dense subset and the global Fano type property. We establish the invariance of Néron-Severi spaces, nef cones, effective cones, movable cones, and Mori chamber decompositions for a family of Fano type varieties after a generically finite base change. Additionally, we show the uniform behavior of the minimal model program for this family. These results are applied to the boundedness problem of Fano type varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04109 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variation of cones of divisors in a family of varieties -- Fano type case Choi, Sung Rak Li, Zhan Zhou, Chuyu Algebraic Geometry We investigate the relationship between the Fano type property on fibers over a Zariski dense subset and the global Fano type property. We establish the invariance of Néron-Severi spaces, nef cones, effective cones, movable cones, and Mori chamber decompositions for a family of Fano type varieties after a generically finite base change. Additionally, we show the uniform behavior of the minimal model program for this family. These results are applied to the boundedness problem of Fano type varieties. |
| title | Variation of cones of divisors in a family of varieties -- Fano type case |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2504.04109 |