Large p-groups actions with a p-elementary abelian second ramification group

Abstract

Let $k$ be an algebraically closed field of characteristic $p>0$ and $C$ a connected nonsingular projective curve over $k$ with genus $g\ge 2$. Let $(C,G)$ be a "big action", i.e. a pair $(C,G)$ where $G$ is a $p$-subgroup of the $k$-automorphism group of $C$ such that$\frac{|G|}{g}>\frac{2p}{p-1}$. We denote by $G_2$ the second ramification group of $G$ at the unique ramification point of the cover $C\to C/G$. The aim of this paper is to describe the big actions whose $G_2$ is $p$-elementary abelian. In particular, we obtain a structure theorem by considering the $k$-algebra generated by the additive polynomials. We more specifically explore the case where there is a maximal number of jumps in the ramification filtration of $G_2$. In this case, we display some universal families.

Cited by in corpus (1)

• Large p-groups actions with |G| /g^2 > 4/ (p^2-1)^2