Moišezon spaces and almost positive coherent sheaves
type: Item
instance of: scholarly article
title: Moišezon spaces and almost positive coherent sheaves
zbMATH Open document ID: 0617.32040
DOI: 10.1007/BF01456958
author: Michael Schneider
published in: Mathematische Annalen
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163804
review text: The main result in this paper is Theorem 2.4: Let X be a compact reduced irreducible normal complex space. X is Moishezon precisely if there exists a (torsion free) coherent sheaf F on X which is almost positive and globally generated. In the case of complex surfaces, the author is able to eliminate the phrase ''globally generated'' from this statement (Theorem 3.3); i.e., he verifies in the affirmative, in the case of dimension 2, Grauert and Riemenschneider's conjectured characterization of Moishezon spaces. The key fact the author uses in the proof of Theorem 2.4 is that if L is a holomorphic line bundle on a compact analytic space \(X^ n\) such that \(c_ 1(L^ n)\) is positive and such that some power of L is globally generated, then X is Moishezon. The author proves this key fact via a straightforward argument involving numerical inequalities. These inequalities yield that the transcendence degree of the field of meromorphic functions on X is equal to n.
Mathematics Subject Classification ID: 32J99
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 32L20
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 4000381
zbMATH Keywords: characterization of Moišezon spaces
zbMATH Keywords: compact irreducible reduced
zbMATH Keywords: normal analytic space
zbMATH Keywords: projective algebraic variety
zbMATH Keywords: almost positive coherent sheaf
MaRDI profile type: Publication
cites work: Espaces Fibres Lineaires Faiblement Negatifs sur un Espace Complexe
cites work: Faisceaux Amples sur les Espaces Analytiques
cites work: On Analytic Surfaces with Two Independent Meromorphic Functions
cites work: Über Modifikationen und exzeptionelle analytische Mengen
cites work: Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen
cites work: Resolution of singularities of an algebraic variety over a field of characteristic zero. I
cites work: Q4154669
cites work: On Kähler varieties of restricted type. (An intrinsic characterization of algebraic varieties.)
cites work: On the Structure of Compact Complex Analytic Surfaces, I
cites work: Über exzeptionelle Mengen
cites work: Erratum et Addendum zu der Arbeit: Über exzeptionelle Mengen
cites work: Moisezon Spaces and Positive Coherent Sheaves
cites work: Characterizing 2-dimensional Moishezon spaces by weakly positive coherent analytic sheaves
cites work: Q4402617
cites work: Characterizing Moišezon spaces by almost positive coherent analytic sheaves
cites work: A generalization of Kodaira's embedding theorem
cites work: Q5570369
cites work: Criteria for quasi-projectivity
cites work: Addendum to `Criteria for quasi-projectivity'
cites work: Classification theory of algebraic varieties and compact complex spaces. Notes written in collaboration with P. Cherenack
description: scientific article; zbMATH DE number 4000381