A differential geometric property of big line bundles
type: Item
instance of: scholarly article
title: A differential geometric property of big line bundles
zbMATH Open document ID: 0802.32027
author: Shigeharu Takayama
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1994-10-16T00:00:00Z
review text: A holomorphic line bundle over a compact complex manifold is shown to be big if it has a singular Hermitian metric whose curvature current is smooth on the complement of some proper analytic subset, strictly positive on some tabular neighborhood of the analytic subset, and satisfies a condition on its integral. In particular, we obtain a sufficient condition for a compact complex manifold to be a Moishezon space.
Mathematics Subject Classification ID: 32J99
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 32L05
zbMATH DE Number: 650901
zbMATH Keywords: big line bundles
zbMATH Keywords: singular Hermitian metric
zbMATH Keywords: Moishezon space
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225762
OpenAlex ID: W1978686583
Wikidata QID: Q115227256
cites work: De Rham cohomology of an analytic space
cites work: Champs magnétiques et inégalités de Morse pour la d''-cohomologie. (Magnetic fields and Morse inequalities for d''-cohomology)
cites work: Closedness of the Douady spaces of compact Kähler spaces
cites work: Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen
cites work: The Extension Problem in Complex Analysis II; Embeddings with Positive Normal Bundle
cites work: Q4195061
cites work: Q3976198
cites work: Currents, metrics and Moishezon manifolds
cites work: Properties of compact complex manifolds carrying closed positive currents
cites work: On 𝑛-dimensional compact complex varieties with 𝑛 algebraically independent meromorphic functions
cites work: Compactification of complete Kähler manifolds of negative Ricci curvature
cites work: Q4185363
cites work: A generalization of Kodaira's embedding theorem
cites work: Vanishing theorems on complex manifolds
cites work: A vanishing theorem for semipositive line bundles over non-Kähler manifolds
cites work: Q3699143
cites work: Classification theory of algebraic varieties and compact complex spaces. Notes written in collaboration with P. Cherenack
cites work: Lectures on Levi convexity of complex manifolds and cohomology vanishing theorems. Notes by M.S.Raghunathan
cites work: Q5677789
DOI: 10.2748/TMJ/1178225762
description: scientific article; zbMATH DE number 650901