Vollständige, fast-vollständige und mengen-theoretisch-vollständige Durchschnitte in Steinschen Mannigfaltigkeiten
type: Item
instance of: scholarly article
title: Vollständige, fast-vollständige und mengen-theoretisch-vollständige Durchschnitte in Steinschen Mannigfaltigkeiten
zbMATH Open document ID: 0532.32005
DOI: 10.1007/BF01457234
author: Michael Schneider
published in: Mathematische Annalen
publication date: 1982-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163664
review text: In the first of four section of this paper the result of \textit{O. Forster} and \textit{K. J. Ramspott} [Invent. Math. 2, 145-170 (1966; Zbl 0154.334)] that every non-singular curve in \({\mathbb{C}}^ 3\) is a complete intersection is extended to the singular case. - The second section is devoted to extending previous results of the author [Math. Ann. 196, 191- 200 (1970; Zbl 0184.110)] also to the singular case. In particular, it is shown that every locally complete intersection Y in a Stein space X with dim Y\(=frac{1}{2}\dim X\) is a complete intersection if and only if the normal bundle of Y is trivial and the dual class d(Y) vanishes. - In the third section the case of codimension two is considered. And the last section consists of applying the results of the first three, along with the Ferrand construction and the Oka principle, in order to find sufficient conditions for a set-theoretic complete intersection (cf. also recent results of C. Bănică and O. Forster).
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 14M10
zbMATH DE Number: 3844119
zbMATH Keywords: Oka principle
zbMATH Keywords: set-theoretic complete intersection
reviewed by: Bruce Gilligan
MaRDI profile type: Publication
cites work: The Riemann-Roch theorem for analytic embeddings
cites work: Riemann-Roch for singular varieties
cites work: Q2546548
cites work: La classe d'homologie fondamentale d'un espace analytique
cites work: Idéaux et modules de fonctions analytiques de variables complexes
cites work: Q4075023
cites work: Primärzerlegung in Steinschen Algebren
cites work: Zur Theorie der Steinschen Algebren und Moduln
cites work: Some remarks on parallelizable Stein manifolds
cites work: Q5736241
cites work: Q5535135
cites work: Okasche Paare von Garben nichtabelscher Gruppen
cites work: Analytische Modulgarben und Endromisbündel
cites work: Homotopieklassen von Idealbasen in Steinschen Algebren
cites work: Über die Anzahl der Erzeugenden von projektiven Steinschen Moduln
cites work: Approximationssaetze für holomorphe Funktionen mit Werten in komplexen Räumen
cites work: Holomorphe Funktionen mit Werten in komplexen Lieschen Gruppen
cites work: Analytische Faserungen über holomorph-vollständigen Räumen
cites work: Q5513537
cites work: Q5521308
cites work: Complete intersections
cites work: Über die Anzahl der Gleichungen, die zur Beschreibung einer algebraischen Varietät nötig sind
cites work: Q3208789
cites work: On the homology groups of Stein spaces
cites work: Vector bundles on complex projective spaces
cites work: Some remarks on Chern classes
cites work: Stetige und holomorphe Schnitte in Bündeln mit homogener Faser
cites work: Lectures on equations defining space curves. Notes by N. Mohan Kumar
Recommended article: Einbettungen Steinscher Mannigfaltigkeiten
Recommended article: Q5541094
Recommended article: Fast-positive Geradenbündel auf kompakten komplexen Mannigfaltigkeiten.
Recommended article: Hochzusammenhängende Mannigfaltigkeiten und ihre Ränder
Recommended article: Q5185629
Recommended article: Q5846368
Recommended article: Q5843103
Recommended article: Q3217191
Recommended article: Q3317548
description: scientific article; zbMATH DE number 3844119