Oka's inequality for currents and applications
type: Item
instance of: scholarly article
title: Oka's inequality for currents and applications
zbMATH Open document ID: 0832.32010
DOI: 10.1007/BF01446636
author: Nessim Sibony
author: J. E. Fornæss
published in: Mathematische Annalen
publication date: 1996-02-26T00:00:00Z
full work available at URL: https://eudml.org/doc/165298
review text: A version of Oka's inequality for currents of the form \(uT\) is given, where \(T\) is a positive closed current of bidimension \((p,p)\) and \(u\) is a negative plurisubharmonic function. It follows that the set where \(uT\) has a locally bounded mass is \(p\)-pseudoconvex (using a convention where \((n - 1)\)-pseudoconvexity is the usual pseudoconvexity). When \(uT\) has a locally bounded mass a convergence result is proved for the operator \[ (u_1 \ldots u_p) \to dd^cu_1 \wedge \cdots \wedge dd^c u_p \wedge T. \] This leads to a Bezout type theorem in \(\mathbb{P}^k\) with an application to holomorphic dynamics in \(\mathbb{P}^k\).
Mathematics Subject Classification ID: 32C30
Mathematics Subject Classification ID: 32F10
Mathematics Subject Classification ID: 32H50
Mathematics Subject Classification ID: 37F99
zbMATH DE Number: 759274
zbMATH Keywords: \(p\)-convexity
zbMATH Keywords: Oka's inequality
zbMATH Keywords: currents
zbMATH Keywords: mass
reviewed by: Daniel Barlet
MaRDI profile type: Publication
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OpenAlex ID: W2080143845
description: scientific article; zbMATH DE number 759274