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.

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