Reduction of the singularities of codimension one singular foliations in dimension three By Felipe Cano Contents 0. Introduction 1. Blowing-up singular foliations . Adapted singular foliations . Permissible centers . Vertical invariants . First properties of presimple singularities 2. Global strategy . Reduction to presimple singularities. Statement . Good points. Bad points. Equi-reduction . Finiteness of bad points . The influency locus . The local control theorem . Destroying cycles . Global criteria of blowing-up 3. Local control . Two-dimensional differential idealistic exponents .
