Projective plane curves whose automorphism groups are simple and primitive

Abstract

We study complex projective plane curves with a given group of automorphisms. Let $G$ be a simple primitive subgroup of $PGL(3,\mathbb{C})$, which is isomorphic to $A_6$, $A_5$ or $PSL(2,{\mathbb{F}}_7)$. We obtain a necessary and sufficient condition on $d$ for the existence of a nonsingular projective plane curve of degree $d$ invariant under $G$. We also study an analogous problem on integral curves.

32 pages

References in corpus (1)

• Automorphism group of plane curve computed by Galois points, II