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, C), which is isomorphic to ₆, ₅ or PSL(2, F₇). 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.