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Stability of foliations induced by rational maps

2010; Cellule MathDoc/CEDRAM; Volume: 18; Issue: 4 Linguagem: Inglês

10.5802/afst.1221

2258-7519

Fernando Cukierman, Jorge Vitório Pereira, Israel Vainsencher,

Meromorphic and Entire Functions

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.