Actions of finite group schemes on curves

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.

Final version, minor changes and corrections. To appear in Pure and Applied Mathematics Quarterly

Cited by in corpus (1)

• Generalizations of quasielliptic curves