On simultaneous uniformization and local nonuniformizability
type: Item
instance of: scholarly article
title: On simultaneous uniformization and local nonuniformizability
zbMATH Open document ID: 1007.32016
DOI: 10.1016/S1631-073X(02)02268-9
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2003-03-12T00:00:00Z
review text: The author shows that there exists an affine algebraic foliation whose universal covering manifold (in short u.c.m.) is not uniformizable. Moreover, each u.c.m. of such a foliation is nowhere locally uniformizable. Furthermore, the above foliation may be chosen such that it is transversally affine and admits a Liouvillian first integral, with dense and hyperbolic leaves and an attractive cycle. Thus, the conjectures of Ilyashenko (stating that each u.c.m. is uniformizable) and of Shcherbakov (stating that each u.c.m. of an algebraic foliation with hyperbolic leaves is locally uniformizable) are given a negative answer.
reviewed by: Eugen Pascu
Mathematics Subject Classification ID: 32Q30
Mathematics Subject Classification ID: 32G13
Mathematics Subject Classification ID: 14J15
Mathematics Subject Classification ID: 14J10
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 32J25
Mathematics Subject Classification ID: 32D99
zbMATH DE Number: 1754782
zbMATH Keywords: universal covering manifold
zbMATH Keywords: projective affine surface
zbMATH Keywords: holomorphic foliation
author: Alexey A. Glutsyuk
MaRDI profile type: Publication
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full work available at URL: s1631-073x(02)02268-9
OpenAlex ID: W2088217990
description: scientific article; zbMATH DE number 1754782