Cyclic Automorphisms groups of genus 10 non-hyperelliptic curves

TL;DR

This paper classifies all cyclic automorphism groups of genus 10 non-hyperelliptic curves and provides explicit equations for each group, covering all such curves with non-trivial automorphisms.

Contribution

It enumerates all cyclic automorphism subgroups for genus 10 non-hyperelliptic curves and supplies explicit defining equations for each group.

Findings

Complete list of cyclic automorphism subgroups for genus 10 non-hyperelliptic curves.

Explicit equations for plane sextic curves with each automorphism group.

Coverage of all non-singular sextic curves with non-trivial automorphisms.

Abstract

In this paper, we list all cyclic automorphisms subgroups $H$ for which there exists a smooth projective non-hyperelliptic sextic curve $C$ with $H\preceq Aut(C)$. Furthermore, we attach to each group a defining equation of a plane sextic curve having exactly this group as cyclic automorphisms subgroup. These equations cover up to isomorphism all plane non-singular sextic curves having some non-trivial automorphism.