An interpolation theorem on cycle spaces for functions arising as integrals of \(\overline{\partial}\)-closed forms
type: Item
instance of: scholarly article
title: An interpolation theorem on cycle spaces for functions arising as integrals of \(\overline{\partial}\)-closed forms
zbMATH Open document ID: 1154.32002
author: Takeo Ohsawa
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2008-09-12T00:00:00Z
review text: When \(M\) is a \((k+1)\)-complete complex manifold the space \(C_k(M)\) of compact \(k\)-cycles in \(M\) is Stein. The author proves a precise and quantitative version of this result interpolating, via the integration on \(k\)-cycles of a \((k,k)\) \(\overline\partial\)-closed form on \(M\) with controlled growth, a sequence of values with suitable growth given on a discrete sequence of \(k\)-cycles in \(C_k(M)\). The proof is based on the \(L^2\) method of Andreotti and Vesentini.
reviewed by: Daniel Barlet
Mathematics Subject Classification ID: 32C30
Mathematics Subject Classification ID: 32F10
Mathematics Subject Classification ID: 14C05
zbMATH DE Number: 5343274
zbMATH Keywords: integration of cohomology classes
zbMATH Keywords: compact cycles
zbMATH Keywords: \(q\)-complete manifold
zbMATH Keywords: \(L^2\) method for \(\overline\partial\)
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1201012373
OpenAlex ID: W2167935509
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DOI: 10.2977/PRIMS/1201012373
description: scientific article; zbMATH DE number 5343274