Global $F$-regularity for weak del Pezzo surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914743598448640 |
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| author | Kawakami, Tatsuro Tanaka, Hiromu |
| author_facet | Kawakami, Tatsuro Tanaka, Hiromu |
| contents | Let $k$ be an algebraically closed field of characteristic $p>0$. Let $X$ be a normal projective surface over $k$ with canonical singularities whose anti-canonical divisor is nef and big. We prove that $X$ is globally $F$-regular except for the following cases: (1) $K_X^2=4$ and $p=2$, (2) $K_X^2=3$ and $p \in \{2, 3\}$, (3) $K_X^2=2$ and $p \in \{2, 3\}$, (4) $K_X^2=1$ and $p \in \{2, 3, 5\}$. For each degree $K_X^2$, the assumption of $p$ is optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04790 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global $F$-regularity for weak del Pezzo surfaces Kawakami, Tatsuro Tanaka, Hiromu Algebraic Geometry 14J45, 13A35 Let $k$ be an algebraically closed field of characteristic $p>0$. Let $X$ be a normal projective surface over $k$ with canonical singularities whose anti-canonical divisor is nef and big. We prove that $X$ is globally $F$-regular except for the following cases: (1) $K_X^2=4$ and $p=2$, (2) $K_X^2=3$ and $p \in \{2, 3\}$, (3) $K_X^2=2$ and $p \in \{2, 3\}$, (4) $K_X^2=1$ and $p \in \{2, 3, 5\}$. For each degree $K_X^2$, the assumption of $p$ is optimal. |
| title | Global $F$-regularity for weak del Pezzo surfaces |
| topic | Algebraic Geometry 14J45, 13A35 |
| url | https://arxiv.org/abs/2404.04790 |