Invariant Hypersurfaces and Nodal Components of Foliations

Abstract

It is known that there is at least an invariant analytic curve passing through each of the components in the complement of nodal singularities, after the reduction of singularities of a germ of singular foliation in ${\mathbb{C}}^2,0$}. Here, we state and prove a generalization of this property to any ambient dimension.

Text and two appendices