Automorphism groups of non-singular plane curves of degree 5

TL;DR

This paper classifies the automorphism groups of non-singular degree 5 plane curves and explores their moduli spaces, extending previous work on quartic curves to degree 5.

Contribution

It determines the non-empty loci of moduli spaces for degree 5 curves with specific automorphism groups, extending known classifications from quartic to quintic curves.

Findings

Identified non-empty loci for automorphism groups of degree 5 curves.

Extended Henn's results from quartic to quintic curves.

Provided explicit descriptions of automorphism groups for degree 5 curves.

Abstract

Henn and Komiya-Kuribayashi listed, independently, the groups $G$ for which $\widetilde{M_3^{Pl}(G)}$ is non-empty. In this paper, we determine the loci $\widetilde{M_6^{Pl}(G)}$, corresponding to non-singular degree $5$ projective plane curves, which are non-empty. Also, we present the analogy of Henn's results for quartic curves concerning non-singular plane model equations associated to these loci.