English

Actions of finite group schemes on curves

Algebraic Geometry 2024-05-21 v2

Abstract

Every action of a finite group scheme GG on a variety admits a projective equivariant model, but not necessarily a normal one. As a remedy, we introduce and explore the notion of GG-normalization. In particular, every curve equipped with a GG-action has a unique projective GG-normal model, characterized by the invertibility of ideal sheaves of all orbits. Also, GG-normal curves occur naturally in some questions on surfaces in positive characteristics.

Keywords

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