Resumen de The moduli space of quadratic rational maps

Laura DeMarco

• Let be the space of quadratic rational maps , modulo the action by conjugation of the group of Möbius transformations. In this paper a compactification of is defined, as a modification of Milnor's , by choosing representatives of a conjugacy class such that the measure of maximal entropy of has conformal barycenter at the origin in and taking the closure in the space of probability measures. It is shown that is the smallest compactification of such that all iterate maps extend continuously to , where is the natural compactification of coming from geometric invariant theory.