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.