The cross-ratio compactification of the configuration space of ordered points on

Abstract

A natural compactification of the virtual configuration space of N points on the Riemann sphere Open image in new window is constructed by using cross-ratios. We show that this compactification is homeomorphic to the Bers’ compactification of the virtual moduli space of a punctured Riemann sphere of type N. In particular, the system of global and explicit coordinates of this standard compactification is given by cross-ratios.