Theta Constants Associated with the Cyclic Triple Coverings of the Complex Projective Line Branching at Six Points

Abstract

Let $\psi$ be the period map for a family of the cyclic triple coverings of the complex projective line branching at six points. The symmetric group $S_6$ acts on this family and on its image under $\psi$. In this paper, we give an $S_6$-equivariant expression of ${\psi }^{-1}$ in terms of fifteen theta constants.