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On the Castelnuovo-Severi inequality.

J.F. Voloch; I. Vainsencher — 1988

Journal für die reine und angewandte Mathematik

Stability of foliations induced by rational maps

F. Cukierman; J. V. Pereira; I. 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 $ℱ_{q} (r, d)$ of singular foliations of codimension $q$ and degree $d$ on the complex projective space $ℙ^{r}$ , when $1 \leq q \leq r - 2$ . 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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