Equivariantly normal varieties for diagonalizable group actions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913357025509376 |
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| author | Brion, Michel |
| author_facet | Brion, Michel |
| contents | Given a finite group scheme $G$ over a field and a $G$-variety $X$, we obtain a criterion for $X$ to be $G$-normal in the sense of \cite{Br24}. When $G$ is diagonalizable, we describe the local structure of $G$-normal varieties in codimension $1$ and their dualizing sheaf. As an application, we obtain a version of the Hurwitz formula for $G$-normal varieties, where $G$ is linearly reductive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12020 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariantly normal varieties for diagonalizable group actions Brion, Michel Algebraic Geometry Commutative Algebra 14L15, 14L30 (Primary) 14E20, 14E22 (Secondary) Given a finite group scheme $G$ over a field and a $G$-variety $X$, we obtain a criterion for $X$ to be $G$-normal in the sense of \cite{Br24}. When $G$ is diagonalizable, we describe the local structure of $G$-normal varieties in codimension $1$ and their dualizing sheaf. As an application, we obtain a version of the Hurwitz formula for $G$-normal varieties, where $G$ is linearly reductive. |
| title | Equivariantly normal varieties for diagonalizable group actions |
| topic | Algebraic Geometry Commutative Algebra 14L15, 14L30 (Primary) 14E20, 14E22 (Secondary) |
| url | https://arxiv.org/abs/2405.12020 |