Non d\'eg\'en\'erescence et singularit\'es des m\'etriques d'Einstein asymptotiquement hyperboliques en dimension 4

摘要

We prove that desingularizations of non degenerate Poincar\'e-Einsteinmetrics with A1 singularities remain non degenerate. In principle this enablesa recursive procedure to desingularize the other Fuchsian singularities. Weillustrate this procedure by the A2 case.