Non straightenable complex lines in \(\mathbb C^2\)
type: Item
instance of: scholarly article
title: Non straightenable complex lines in \(\mathbb C^2\)
zbMATH Open document ID: 0853.58015
DOI: 10.1007/BF02559509
author: Franc Forstnerič
author: Josip Globevnik
author: Jean-Pierre Rosay
published in: Arkiv för Matematik
publication date: 1997-01-05T00:00:00Z
review text: It is known that if \(P\) is a polynomial embedding of \(\mathbb C\) into \(\mathbb C^2\), then there exists \(\psi\), a polynomial automorphism of \(\mathbb C^2\), such that \((\psi \circ P) (\mathbb C) = \mathbb C \times \{0\}\). The main result of the paper is contained in the following. Proposition 1. Let \(n>1\). There exists a proper holomorphic embedding \(H : \mathbb C \to \mathbb C^n\) such that for no automorphism \(\psi\) of \(\mathbb C^n\) \((\psi \circ H) (\mathbb C) = \mathbb C \times \{0\} \subset \mathbb C^n\).
Mathematics Subject Classification ID: 32H02
Mathematics Subject Classification ID: 58C10
Mathematics Subject Classification ID: 32H35
zbMATH DE Number: 896434
zbMATH Keywords: polynomial embedding
zbMATH Keywords: polynomial automorphism
zbMATH Keywords: holomorphic embedding
reviewed by: Vasil G. Angelov
MaRDI profile type: Publication
cites work: Q4097032
cites work: On the group of holomorphic automorphisms of \(\mathbb{C}{}^ n\)
cites work: Approximation of biholomorphic mappings by automorphisms of \(\mathbb{C}^ n\)
cites work: Holomorphic embeddings of planar domains in \(\mathbb{C}^ 2\)
cites work: L'image d'une application holomorphe
cites work: The extension of regular and rational embeddings
cites work: Propriétés topologiques des polynômes de deux variables complexes et automorphismes algébriques de l'espace \(C^2\)
description: scientific article; zbMATH DE number 896434