Rigidity for Dicritical Germ of Foliation in C

We study some kind of rigidity property for dicritical foliation in C 2 thanks to a new meromorphic function associated to any dicriti-cal foliation playing the role of equation of separatrix. To be more specific, we compute infinitesimal obstructions for realizing the holon-omy pseudo-group of a dicritical foliation F on any source manifold of a blowing-up morphism with same dual tree as the desingularization of F. Using two examples, we remark that these obstructions come from some analytical invariants shared by the space of leaves and the ambient space. This situation never occurs in the non-dicritical case.