A short analytic proof of closedness of logarithmic forms
type: Item
instance of: scholarly article
title: A short analytic proof of closedness of logarithmic forms
zbMATH Open document ID: 0841.32005
author: Junjiro Noguchi
published in: Kodai Mathematical Journal
publication date: 1996-02-01T00:00:00Z
review text: Theorem: Let \(D\) be an effective reduced divisor on a compact Kähler manifold \(M\), let \(\omega\) be a logarithmic \(p\)-form over \(M\) along \(D\). Then \(d \omega = 0\) in \(M \backslash D\). Deligne proved it for \(M\) being complex projective by showing the degeneracy of a certain spectral sequence. In fact, his proof gives the result for a general \(M\). The author gives the theorem an analytic proof. He uses the desingularization theorem by Hironaka to assume that \(D\) has simple normal crossings only and then he proceeds by induction on \(p\) using the classical harmonic integral theory.
Mathematics Subject Classification ID: 32C30
Mathematics Subject Classification ID: 32C25
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 58A14
zbMATH DE Number: 840320
zbMATH Keywords: logarithmic form
zbMATH Keywords: Kähler manifold
zbMATH Keywords: desingularization
zbMATH Keywords: harmonic integral
reviewed by: Krzysztof Dabrowski
MaRDI profile type: Publication
OpenAlex ID: W2059400413
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DOI: 10.2996/KMJ/1138043426
description: scientific article; zbMATH DE number 840320