Pull-back components of the space of foliations of codimension $\ge 2$

We present a new list of irreducible components for the space of k-dimensional holomorphic foliations on ${\mathbb{P}}^n$, $n\ge 3$, $k\ge 2$. They are associated to pull-back of dimension one foliations on $\mathbb P^{n-k+1}$ by non-linear rational maps.