Deformations of holomorphic foliations having a meromorphic first integral.
Dicritical logarithmic foliations.
We show the existence of weak logarithmic models for any (dicritical or not) holomorphic foliation F of (C2,0) without saddle-nodes in its desingularization. The models are written in terms of a representative set of separatrices, whose equisingularity types are controlled by the Milnor number of the foliation.
Diophantine approximations and foliations