Preprint A552/2007
Frobenius theorem for foliations on singular varieties

Dominique Cerveau | Lins Neto , Alcides

**Keywords: **

We generalize Frobenius singular theorem due to Malgrange, for a large class of codimension one holomorphic foliations on singular analytic subsets of $\C^N$. As a consequence we obtain the following : let $M$ be a smooth complete intersection sub-variety of $\Bbb{P}^N$, where $dim(M)\ge 3$. Then the singular set of any codimension one foliation on $M$ has at least one component of codimension two.