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arXiv · 0709.4072

Stability of foliations induced by rational maps

F. Cukierman·J. V. Pereira·I. Vainsencher
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Abstract

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.

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F. Cukierman, J. V. Pereira, I. Vainsencher. 2007-09-26. Stability of foliations induced by rational maps. https://arxiv.org/abs/0709.4072

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