A topological characterization of \({\mathbb{C}}^ 2/G\)
type: Item
instance of: scholarly article
title: A topological characterization of \({\mathbb{C}}^ 2/G\)
zbMATH Open document ID: 0602.14037
published in: Journal of Mathematics of Kyoto University
publication date: 1985-01-01T00:00:00Z
review text: It is shown that an affine normal surface V which is topologically contractible and has a finite fundamental group at infinity \(\pi_ 1^{\infty}(V)\) is isomorphic to \({\mathbb{C}}^ 2/G\), where G is a small subgroup of Gl(2,\({\mathbb{C}})\), isomorphic to \(\pi_ 1^{\infty}(V)\). Examples show that none of the assumption can be removed. The proof rests on a generalization, due to Nori, of the Lefschetz hyperplane section theorem, on classical results of Kodaira concerning elliptic fibrations, and on a previous paper of the authors, proving the converse of the above result.
Mathematics Subject Classification ID: 14J15
Mathematics Subject Classification ID: 14L17
Mathematics Subject Classification ID: 32M05
zbMATH DE Number: 3970922
zbMATH Keywords: fundamental group at infinity
zbMATH Keywords: quotient of complex 2-space
zbMATH Keywords: Lefschetz hyperplane section theorem
zbMATH Keywords: elliptic fibrations
author: Rajendra Gurjar
author: Anant R. Shastri
reviewed by: Frédéric Campana
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250521023
OpenAlex ID: W1570437781
DOI: 10.1215/KJM/1250521023
description: scientific article; zbMATH DE number 3970922