Complex projective foliations having sub-exponential growth
type: Item
instance of: scholarly article
title: Complex projective foliations having sub-exponential growth
zbMATH Open document ID: 1008.32016
DOI: 10.1016/S0019-3577(01)80011-2
published in: Indagationes Mathematicae. New Series
publication date: 2002-07-11T00:00:00Z
review text: Let \(X\) be a polynomial vector field on the complex plane, and denote by \({\mathcal F}\) the corresponding holomorphic foliation on the complex projective plane. Assume that \({\mathcal F}\) has hyperbolic singularities and for some Riemannian metric (hermitian along the leaves), these leaves have sub-exponential growth. The author shows that \({\mathcal F}\) arose from a linear and hyperbolic polynomial vector field, on some suitable affine chart. In particular, the limit set of the foliation is a union of singularities and algebraic leaves. The author uses the classical ideas of J. Plante on the growth of the leaves for real foliations. This is a nice application, since this technique is almost unexplored for holomorphic foliations.
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 1766471
zbMATH Keywords: holomorphic foliations
zbMATH Keywords: growth of the leaves
author: Bruno Scárdua
reviewed by: Jesus Muciño Raymundo
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1766471