In this article, for holomorphic foliations of codimension one at (C 3 , 0), we define the family of second type foliations. This is formed by foliations having, in the reduction process by blow-up maps, only well oriented singularities, meaning that the reduction divisor does not contain weak separatrices of saddle-node singularities. We prove that the reduction of singularities of a non-dicritical foliation of second type coincides with the desingularization of its set of separatrices.

No abstract

Given a foliation F on P 2 C , by fixing a line L ⊂ P 2 C , the polar pencil of F with axis L is the set of all polar curves of F with respect to points l ∈ L. In this work we study foliations F which admit a polar pencil whose generic element is reducible. To such an F is associated a primitive model, which is a foliation F whose polar pencil, besides having irreducible generic element, is such that its fibers are contained in those of the polar pencil of F. This work focuses on relating geometric properties of a foliation F with those of its primitive model F .