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Stability of foliations induced by rational maps

F. CukiermanJ. V. PereiraI. Vainsencher — 2009

Annales de la faculté des sciences de Toulouse Mathématiques

We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space q ( r , d ) of singular foliations of codimension q and degree d on the complex projective space 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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