On the density of the Pfaffian systems without algebraic solution
type: Item
instance of: scholarly article
title: On the density of the Pfaffian systems without algebraic solution
zbMATH Open document ID: 0792.58001
author: Marcos Sebastiani
author: Luís Gustavo Mendes
publication date: 1994-08-07T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75058
review text: Let \(M\) be an analytic surface. \textit{A. Lins Neto} [J. Differ. Geom. 26, 1-31 (1987; Zbl 0625.57012)] introduced a topology in the set \(\Pi(M)\) of holomorphic foliations with isolated singularities on \(M\). \(\Omega \in \Pi(M)\) is ``rigid'' if it is an isolated point of \(\Pi(M)\). In our paper it is proved that if \(M\) is a projective rational surface non-isomorphic to \(\mathbb{P}_ 2(\mathbb{C})\) then there exists \(\Omega \in \Pi(M)\) rigid and having algebraic leaves. The case of \(\mathbb{P}_ 2(\mathbb{C})\) has been considered by \textit{J. P. Jouanolou} [`Equations de Pfaff algébriques' (1979; Zbl 0477.58002)].
Mathematics Subject Classification ID: 58A17
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 37C85
zbMATH DE Number: 566972
zbMATH Keywords: holomorphic foliations
zbMATH Keywords: projective rational surface
MaRDI profile type: Publication
OpenAlex ID: W1977791781
cites work: Construction of singular holomorphic vector fields and foliations in dimension two
cites work: Equations de Pfaff algébriques
cites work: Q4175362
cites work: Invariant varieties through singularities of holomorphic vector fields
DOI: 10.5802/AIF.1397
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 566972