Mathematics – Algebraic Geometry
Scientific paper
2007-09-26
Annales de la facult\'e des sciences de Toulouse S\'er. 6, 18 no. 4 (2009), p. 685-715
Mathematics
Algebraic Geometry
Scientific paper
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.
Cukierman Fernando
Pereira Jorge Vitório
Vainsencher Israel
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