The space of marked n distinct points on the complex
projective line up to projective transformations will be called a
configuration space. There are two families of complex hyperbolic structures on the configuration space constructed by Deligne-
Mostow and by Thurston. We review that these families are the
same, and then exhibit the families for n = 4, 5 in constrast with
the deformation theory of real hyperbolic cone 3-manifolds.
