Rigidity for dicritical germ of foliation in C2

Considering the problem of moduli for a germ of singular holomorphic foliation in C-2 leads naturally to point out some of its analytical invariants: the reduction of its singularities and the collection of its projective holonomy representations. It is of interest to know whether any coherent data of these invariants can be realized in a concrete foliation. The aim of this paper is to provide the infinitesimal obstructions to this problem for dicritical foliations, in sharp contrast with the non-dicritical case previously studied in [2].