Actions of finite group schemes on curves

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.

Full Text (PDF format)

Received 17 July 2022

Received revised 29 November 2022

Accepted 2 February 2023

Published 15 May 2024