Dicritical logarithmic foliations

We show the existence of weak logarithmic models for any (dicritical or not) holomorphic foliation $\mathcal F$ of $({\mathbb C}^2,0)$ 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.