Linear pencils of foliations over \(\mathbb{C}\mathbb{P}(3)\) and Brunella's conjecture
type: Item
instance of: scholarly article
title: Linear pencils of foliations over \(\mathbb{C}\mathbb{P}(3)\) and Brunella's conjecture
zbMATH Open document ID: 1023.32017
DOI: 10.5565/PUBLMAT_46202_06
published in: Publicacions Matemàtiques
publication date: 2003-11-04T00:00:00Z
full work available at URL: https://eudml.org/doc/41459
review text: The conjecture of Brunella states that if \(\mathcal F\) is a holomorphic foliation of codimension one on \(\mathbb{C} P(3)\), then either \(\mathcal F\) has an invariant surface or there exists a (singular) holomorphic foliation \(\mathcal G\) whose leaves are Riemann surfaces which are contained in those ones of \(\mathcal F\) and their closures are algebraic. The author shows that this conjecture holds for a generic element of a linear pencil of codimension one foliations of degree \( \nu \) . A very interesting discussion on the conjecture, its relations with other results and on generalisations to higher dimensions is also presented.
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 37F75
zbMATH DE Number: 1876878
zbMATH Keywords: linear pencils of foliations
zbMATH Keywords: projective space
Wikidata QID: Q123262637
author: Dominique Cerveau
reviewed by: Eugen Pascu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1876878