Curves with more than one inner Galois point

Gábor Korchmáros; Stefano Lia; Marco Timpanella

paper

Curves with more than one inner Galois point

arXiv:1902.10201

Abstract

Let $C$ be an irreducible plane curve of $PG (2, K)$ where $K$ is an algebraically closed field of characteristic $p \geq 0$ . A point $Q \in C$ is an inner Galois point for $C$ if the projection $π_{Q}$ from $Q$ is Galois. Assume that $C$ has two different inner Galois points $Q_{1}$ and $Q_{2}$ , both simple. Let $G_{1}$ and $G_{2}$ be the respective Galois groups. Under the assumption that $G_{i}$ fixes $Q_{i}$ , for $i = 1, 2$ , we provide a complete classification of $G = ⟨ G_{1}, G_{2} ⟩$ and we exhibit a curve for each such $G$ . Our proof relies on deeper results from group theory.