The Automorphism Group and Invariants of a Curve of Genus 2

Abstract

Let M be a curve of genus 2 over $\mathbb{C}$, and let V be the hyperelliptic involution of M. Assume Aut(M)$\supsetneqq \left\langle V \right\rangle$. Then Aut(M)/$\left\langle V \right\rangle$ is a non-trivial finite subgroup of Aut($\mathbb{P}^1$). It is well-known that finite subgroups H of Aut($\mathbb{P}^1$) are classified into five types. In [8], we determined the defining equations of M with H = Aut(M)/$\left\langle V \right\rangle$ for each type of H. In this paper we study invariants of M derived from these equations.