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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2308.08122 |
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| _version_ | 1866912054395273216 |
|---|---|
| author | Tanaka, Hiromu |
| author_facet | Tanaka, Hiromu |
| contents | Let $X$ be a smooth Fano threefold over an algebraically closed field of positive characteristic. Assume that $|-K_X|$ is very ample and each of the index and the Picard number is equal to one. We prove that $3 \leq g \leq 12$ and $g \neq 11$ for the genus $g$ of $X$. Moreover, we show that there exists no smooth curve on $X$ along which the blowup is Fano. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08122 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fano threefolds in positive characteristic II Tanaka, Hiromu Algebraic Geometry Let $X$ be a smooth Fano threefold over an algebraically closed field of positive characteristic. Assume that $|-K_X|$ is very ample and each of the index and the Picard number is equal to one. We prove that $3 \leq g \leq 12$ and $g \neq 11$ for the genus $g$ of $X$. Moreover, we show that there exists no smooth curve on $X$ along which the blowup is Fano. |
| title | Fano threefolds in positive characteristic II |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2308.08122 |