Approximation of currents on complex manifolds
type: Item
instance of: scholarly article
title: Approximation of currents on complex manifolds
zbMATH Open document ID: 0924.32014
author: Vincent Guedj
published in: Mathematische Annalen
publication date: 1999-01-01T00:00:00Z
full work available at URL: https://zenodo.org/record/1039771
review text: We prove approximation results, on projective algebraic and Stein manifolds, of positive closed currents of bidegree (1,1) by rational divisors with a control on their support and Lelong numbers. We define a notion of (strong-)rational convexity on complex manifolds and show that a totally real compact submanifold \(S\) of a projective algebraic (resp. a Stein) manifold \(X\) is rationally convex iff there is a Hodge form \(\omega\) on \(X\) s.t. \(\omega|_S\equiv 0\), generalizing a theorem of Duval and Sibony.
Mathematics Subject Classification ID: 32E20
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32C20
zbMATH DE Number: 1295411
zbMATH Keywords: projective algebraic manifolds
zbMATH Keywords: line bundle
zbMATH Keywords: rational convexity
zbMATH Keywords: approximation
zbMATH Keywords: Stein manifolds
zbMATH Keywords: positive closed currents
MaRDI profile type: Publication
OpenAlex ID: W2117750866
DOI: 10.1007/S002080050269
description: scientific article; zbMATH DE number 1295411