Codimension one holomorphic foliations on ${\mathbb{P}}_{\mathbb{C}}^n$: problems in complex geometry

Abstract

After a short review on foliations, we prove that a codimension 1 holomorphic foliation on ${\mathbb{P}}_{\mathbb{C}}^3$ with simple singularities is given by a closed rational 1-form. The proof uses Hironaka-Matsumura prolongation theorem of formal objects.