Einbettungen Steinscher Mannigfaltigkeiten
type: Item
instance of: scholarly article
title: Einbettungen Steinscher Mannigfaltigkeiten
zbMATH Open document ID: 0544.32006
DOI: 10.1007/BF01174592
author: Ulrich Schafft
published in: Manuscripta Mathematica
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155010
review text: Let X be a Stein manifold of dimension n. A well-known conjecture in geometric function theory is the conjecture of Forster, namely that there exists an embedding of X in an affine space \({\mathbb{C}}^ N\) for \(N=n+1+[n/2]\). Forster has proved the existence of an embedding of X in \({\mathbb{C}}^ N\) for \(N=2n-[(n-2)/3]\) and \(n\geq 6\) [\textit{O. Forster}, Comm. Math. Helvet. 45, 170-184 (1970; Zbl 0184.314)]. In this paper an amelioration of Forster's result is given. For example, there exists an embedding of X in \({\mathbb{C}}^ N\) for \(N=2n-[2(n-5)/5]\) and \(n\geq 15\). Better bounds are given for greater n. Finally, it is proved that Forster's conjecture holds 'asymptotically'.
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 14E25
Mathematics Subject Classification ID: 57R42
zbMATH DE Number: 3865696
zbMATH Keywords: embedding of Stein manifold
Wikidata QID: Q106421081
MaRDI profile type: Publication
cites work: Nonsingular mappings of Stein manifolds
cites work: Vollständige, fast-vollständige und mengen-theoretisch-vollständige Durchschnitte in Steinschen Mannigfaltigkeiten
OpenAlex ID: W2043774721
description: scientific article; zbMATH DE number 3865696