Codimension one holomorphic foliations on $\mathbb P^n_{\mathbb C}$:   problems in complex geometry
  After a short review on foliations, we prove that a codimension 1 holomorphic foliation on $\mathbb P^3_{\mathbb C}$ with simple singularities is given by a closed rational 1-form. The proof uses Hironaka-Matsumura prolongation theorem of formal objects. 
Dominique Cerveau
math.DS