Actions of finite group schemes on curves
Algebraic Geometry
2024-05-21 v2
Abstract
Every action of a finite group scheme on a variety admits a projective equivariant model, but not necessarily a normal one. As a remedy, we introduce and explore the notion of -normalization. In particular, every curve equipped with a -action has a unique projective -normal model, characterized by the invertibility of ideal sheaves of all orbits. Also, -normal curves occur naturally in some questions on surfaces in positive characteristics.
Cite
@article{arxiv.2207.08209,
title = {Actions of finite group schemes on curves},
author = {Michel Brion},
journal= {arXiv preprint arXiv:2207.08209},
year = {2024}
}
Comments
Final version, minor changes and corrections. To appear in Pure and Applied Mathematics Quarterly