Frobenius theorem for foliations on singular varieties
type: Item
instance of: scholarly article
title: Frobenius theorem for foliations on singular varieties
zbMATH Open document ID: 1194.32018
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2009-10-19T00:00:00Z
review text: In this paper, the authors present a generalization of Malgrange's Frobenius Singular Theorem to certain germs of analytic foliations of germs of irreducible analytic subsets \(X\) of \(\mathbb{C}^N\). A particular case of interest is where \(X\) is a complete intersection and \(\mathrm{dim}(\mathrm{sing}(X))\leq \mathrm{dim}(X)-3\). The proof uses in particular a construction by Godbillon of a \textit{Godbillon-Vey sequence} associated to an integrable \(1\)-form \(\omega\) satisfying \(\mathrm{cod}(\mathrm{sing}(\omega))\geq 3\).
reviewed by: Athanase Papadopoulos
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 32C25
Mathematics Subject Classification ID: 32B10
zbMATH DE Number: 5617950
zbMATH Keywords: Frobenius theorem
zbMATH Keywords: holomorphic foliation
zbMATH Keywords: complex singularities
author: Dominique Cerveau
author: A. Lins Neto
MaRDI profile type: Publication
full work available at URL: s00574-008-0016-2
OpenAlex ID: W2074409964
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DOI: 10.1007/S00574-008-0016-2
description: scientific article; zbMATH DE number 5617950