Actions of finite group schemes on curves
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929347233841152 |
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| author | Brion, Michel |
| author_facet | Brion, Michel |
| contents | Every action of a finite group scheme $G$ on a variety admits a projective equivariant model, but not necessarily a normal one. As a remedy, we introduce and explore the notion of $G$-normalization. In particular, every curve equipped with a $G$-action has a unique projective $G$-normal model, characterized by the invertibility of ideal sheaves of all orbits. Also, $G$-normal curves occur naturally in some questions on surfaces in positive characteristics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_08209 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Actions of finite group schemes on curves Brion, Michel Algebraic Geometry 14L15, 14L30 (Primary) 14E07, 14H37, 14J50 (Secondary) Every action of a finite group scheme $G$ on a variety admits a projective equivariant model, but not necessarily a normal one. As a remedy, we introduce and explore the notion of $G$-normalization. In particular, every curve equipped with a $G$-action has a unique projective $G$-normal model, characterized by the invertibility of ideal sheaves of all orbits. Also, $G$-normal curves occur naturally in some questions on surfaces in positive characteristics. |
| title | Actions of finite group schemes on curves |
| topic | Algebraic Geometry 14L15, 14L30 (Primary) 14E07, 14H37, 14J50 (Secondary) |
| url | https://arxiv.org/abs/2207.08209 |