Stability of foliations induced by rational maps

Abstract

We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space ℱ q (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.