%0 Journal Article
%T Stability of foliations induced by rational maps
%A F. Cukierman
%A J. V. Pereira
%A I. Vainsencher
%J Mathematics
%D 2007
%I arXiv
%X We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space $\mathscr F_q(r, d)$ of singular foliations of codimension $q$ and degree $d$ on the complex projective space $\mathbb P^r$, when $1\le q \le r-2$. 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.
%U http://arxiv.org/abs/0709.4072v1