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We present a new list of irreducible components for the space ofk-dimensional holomorphic foliations on $\mathbb P^{n}$, $n\geq3$, $k\ge2$.They are associated to pull-back of dimension one foliations on $\mathbbP^{n-k+1}$ by non-linear rational maps.

Pull-back components of the space of foliations of codimension $\ge2$