Projective varieties with nef tangent bundle in positive characteristic
| Autor: | Kanemitsu, Akihiro, Watanabe, Kiwamu |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $X$ be a smooth projective variety defined over an algebraically closed field of positive characteristic $p$ whose tangent bundle is nef. We prove that $X$ admits a smooth morphism $X \to M$ such that the fibers are Fano varieties with nef tangent bundle and $T_M$ is numerically flat. We also prove that extremal contractions exist as smooth morphisms. As an application, we prove that, if the Frobenius morphism can be lifted modulo $p^2$, then $X$ admits, up to a finite \'etale Galois cover, a smooth morphism onto an ordinary abelian variety whose fibers are products of projective spaces. Comment: 24 pages |
| Databáze: | arXiv |
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