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arXiv · 2207.08209

Actions of finite group schemes on curves

Michel Brion
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Abstract

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.

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Michel Brion. 2024-05-20. Actions of finite group schemes on curves. https://arxiv.org/abs/2207.08209

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