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Abstract. We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space Fq(r, d) of singular foliations of codimension q and degree d on the complex projective space P r , when 1 ≤ q ≤ r − 2. We study the geometry of these irreducible components. In particular we prove that they are all rational varieties and we compute their projective degrees in several cases.

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A logarithmic 1-form on CP n can be written as, the singularities of ω consist of a schematic union of the codimension 2 subvarieties F i = F j = 0 together with, possibly, finitely many isolated points. This is the case when all F i are smooth and in general position. In this situation, we give a formula which prescribes the number of isolated singularities.

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