| Résume | It is classically known that germs of plane holomorphic foliations always have an invariant curve. By contrast, in ambient dimension three there exist germs of codimension one holomorphic foliations that do not have an invariant surface; the common feature they share is the appearance of compact dicritical components after any procedure of reduction of singularities. Brunella’s Alternative, in its local version, deals with the question of how much transcendental the leaves of such a foliations can be. In this talk, we introduce some of the main ingredients involved in the study of this problem. |
