Endomorphisms of varieties and Bott vanishing
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916203810783232 |
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| author | Kawakami, Tatsuro Totaro, Burt |
| author_facet | Kawakami, Tatsuro Totaro, Burt |
| contents | We show that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. This is a new way to analyze which varieties have nontrivial endomorphisms. In particular, we extend some classification results on varieties admitting endomorphisms (for Fano threefolds of Picard number one and several other cases) to any characteristic. The classification results in characteristic zero are due to Amerik-Rovinsky-Van de Ven, Hwang-Mok, Paranjape-Srinivas, Beauville, and Shao-Zhong. Our method also bounds the degree of morphisms into a given variety. Finally, we relate endomorphisms to global $F$-regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11921 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Endomorphisms of varieties and Bott vanishing Kawakami, Tatsuro Totaro, Burt Algebraic Geometry 14F17, 14J45, 14J70, 08A35 We show that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. This is a new way to analyze which varieties have nontrivial endomorphisms. In particular, we extend some classification results on varieties admitting endomorphisms (for Fano threefolds of Picard number one and several other cases) to any characteristic. The classification results in characteristic zero are due to Amerik-Rovinsky-Van de Ven, Hwang-Mok, Paranjape-Srinivas, Beauville, and Shao-Zhong. Our method also bounds the degree of morphisms into a given variety. Finally, we relate endomorphisms to global $F$-regularity. |
| title | Endomorphisms of varieties and Bott vanishing |
| topic | Algebraic Geometry 14F17, 14J45, 14J70, 08A35 |
| url | https://arxiv.org/abs/2302.11921 |