
Mathematics 2008
Large pgroups actions with a pelementary abelian second ramification groupAbstract: Let $k$ be an algebraically closed field of characteristic $p>0$ and $C$ a connected nonsingular projective curve over $k$ with genus $g \geq 2$. 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$\frac{G}{g} >\frac{2 p}{p1}$. 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.
