Configuration spaces of points on the circle and hyperbolic Dehn fillings

A purely combinatorial compactification of the configuration space of n(gre ater than or equal to 5) distinct points with equal weights in the real pro jective line was introduced by M. Yoshida. We geometrize it so that it will be a real hyperbolic cone-manifold of finite volume with dimension n - 3. Then, we vary weights for points. The geometrization still makes sense and yields a deformation. The effectivity of deformations arisen in this manner will be locally described in the existing deformation theory of hyperbolic structures when n - 3 = 2, 3. (C) 1999 Elsevier Science Ltd. All rights re served.