Bertini's theorem for $F$-rational $F$-pure singularities
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866911183385133056 |
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| author | De Stefani, Alessandro Polstra, Thomas Simpson, Austyn |
| author_facet | De Stefani, Alessandro Polstra, Thomas Simpson, Austyn |
| contents | Let $k$ be an algebraically closed field of characteristic $p>0$, and let $X\subseteq\mathbb{P}^n_k$ be a quasi-projective variety that is $F$-rational and $F$-pure. We prove that if $H \subseteq \mathbb{P}^n_k$ is a general hyperplane, then $X \cap H$ is also $F$-rational and $F$-pure. Of related but independent interest, we present a relationship between the characteristic and index of a $\mathbb{Q}$-Gorenstein variety with isolated non-$F$-regular locus which is $F$-pure but not $F$-regular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04433 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bertini's theorem for $F$-rational $F$-pure singularities De Stefani, Alessandro Polstra, Thomas Simpson, Austyn Algebraic Geometry Commutative Algebra Let $k$ be an algebraically closed field of characteristic $p>0$, and let $X\subseteq\mathbb{P}^n_k$ be a quasi-projective variety that is $F$-rational and $F$-pure. We prove that if $H \subseteq \mathbb{P}^n_k$ is a general hyperplane, then $X \cap H$ is also $F$-rational and $F$-pure. Of related but independent interest, we present a relationship between the characteristic and index of a $\mathbb{Q}$-Gorenstein variety with isolated non-$F$-regular locus which is $F$-pure but not $F$-regular. |
| title | Bertini's theorem for $F$-rational $F$-pure singularities |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2509.04433 |