The moduli space of 8 points on ${\bf P}^1$ and automorphic forms

Abstract

First we give a complex ball uniformization of the moduli space of 8 ordered points on the projective line by using the theory of periods of K3 surfaces. Next we give a projective model of this moduli space by using automorphic forms on a bounded symmetric domain of type IV which coincides with the one given by cross ratios of 8 ordered points of the projective line.