General hyperplane sections of log canonical threefolds in positive characteristic
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908541222125568 |
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| author | Sato, Kenta |
| author_facet | Sato, Kenta |
| contents | In this paper, we prove that if a $3$-dimensional quasi-projective variety $X$ over an algebraically closed field of characteristic $p>3$ has only log canonical singularities, then so does a general hyperplane section $H$ of $X$. We also show that the same is true for klt singularities, which is a slight extension of \cite{ST20}. In the course of the proof, we provide a sufficient condition for log canonical (resp.~klt) surface singularities to be geometrically log canonical (resp.~geometrically klt) over a field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_14599 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | General hyperplane sections of log canonical threefolds in positive characteristic Sato, Kenta Algebraic Geometry Commutative Algebra 14B05, 14J17 In this paper, we prove that if a $3$-dimensional quasi-projective variety $X$ over an algebraically closed field of characteristic $p>3$ has only log canonical singularities, then so does a general hyperplane section $H$ of $X$. We also show that the same is true for klt singularities, which is a slight extension of \cite{ST20}. In the course of the proof, we provide a sufficient condition for log canonical (resp.~klt) surface singularities to be geometrically log canonical (resp.~geometrically klt) over a field. |
| title | General hyperplane sections of log canonical threefolds in positive characteristic |
| topic | Algebraic Geometry Commutative Algebra 14B05, 14J17 |
| url | https://arxiv.org/abs/2303.14599 |