English

Branched pull-back components of the space of codimension 1 foliations on $\mathbb P^n$

Complex Variables 2015-03-27 v1 Algebraic Geometry Dynamical Systems

Abstract

Let F\mathcal{F} be written as fG f^{*}\mathcal{G}, where G\mathcal{G} is a foliation in P2 {\mathbb P^2} with three invariant lines in general position, say (XYZ)=0(XYZ)=0, and f:Pn>P2f:{\mathbb P^n}--->{\mathbb P^2}, f=(F0α:F1β:F2γ)f=(F^\alpha_{0}:F^\beta_{1}:F^\gamma_{2}) is a nonlinear rational map. Using local stability results of singular holomorphic foliations, we prove that: if n3n\geq 3, the foliation F\mathcal{F} is globally stable under holomorphic deformations. As a consequence we obtain new irreducible componentes for the space of codimension one foliations on Pn\mathbb P^n. We present also a result which characterizes holomorphic foliations on Pn,n3{\mathbb P^n}, n\geq 3 which can be obtained as a pull back of foliations on P2 {\mathbb P^2} of degree d2d\geq2 with three invariant lines in general position.

Keywords

Cite

@article{arxiv.1503.07827,
  title  = {Branched pull-back components of the space of codimension 1 foliations on $\mathbb P^n$},
  author = {W. Costa e Silva},
  journal= {arXiv preprint arXiv:1503.07827},
  year   = {2015}
}

Comments

arXiv admin note: text overlap with arXiv:1503.00715