English

Stability of branched pull-back projective foliations

Complex Variables 2015-03-30 v1 Algebraic Geometry Dynamical Systems

Abstract

We prove that, if n3n\geq 3, a singular foliation F\mathcal{F} on Pn\mathbb P^n which can be written as pull-back, where G\mathcal{G} is a foliation in P2 {\mathbb P^2} of degree d2d\geq2 with one or three invariant lines in general position and f:Pn>P2f:{\mathbb P^n}--->{\mathbb P^2}, deg(f)=ν2,deg(f)=\nu\geq2, is an appropriated rational map, is stable under holomorphic deformations. As a consequence we conclude that the closure of the sets {F=f(G)}\{\mathcal {F}= f^{*}(\mathcal{G})\} are new irreducible components of the space of holomorphic foliations of certain degrees.

Keywords

Cite

@article{arxiv.1503.07923,
  title  = {Stability of branched pull-back projective foliations},
  author = {W. Costa e Silva},
  journal= {arXiv preprint arXiv:1503.07923},
  year   = {2015}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1503.07827, arXiv:1503.00715

R2 v1 2026-06-22T09:03:20.497Z