Actions of finite group schemes on curves

DOI10.4310/PAMQ.2024.V20.N3.A2arXiv2207.08209OpenAlexW4396941666MaRDI QIDQ6405224

Michel Brion

Publication date: 17 July 2022

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.

Full work available at URL: https://doi.org/10.4310/pamq.2024.v20.n3.a2

Mathematics Subject Classification ID

Birational automorphisms, Cremona group and generalizations (14E07) Group actions on varieties or schemes (quotients) (14L30) Automorphisms of curves (14H37) Automorphisms of surfaces and higher-dimensional varieties (14J50) Group schemes (14L15)

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