2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78864The space of marked n distinct points on the complex projective line up to projective transformations will be called a configuration space in this paper. There are two families of complex hyperbolic structures on the configuration space constructed by Deligne-Mostow and Thurston. We first confirm that these families are the same. Then in view of the deformation theory for real hyperbolic cone 3-manifolds, we review the families for small n.11 pagesGeometric TopologyAlgebraic Geometry57M50 (Primary); 14D25, 14D30, 32M10, 53C56 (Secondary)text