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Pure and Applied Mathematics Quarterly
Volume 20 (2024)
Number 3
Special Issue in Honor of Claudio Procesi
Guest Editors: Luca Migliorini, Paolo Papi, and Mario Salvetti
Actions of finite group schemes on curves
Pages: 1065 – 1095
DOI: https://dx.doi.org/10.4310/PAMQ.2024.v20.n3.a2
Author
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.
Keywords
finite group scheme, curve, surface
2010 Mathematics Subject Classification
Primary 14L15, 14L30. Secondary 14E07, 14H37, 14J50.
Received 17 July 2022
Received revised 29 November 2022
Accepted 2 February 2023
Published 15 May 2024