Hodge spectral sequence and symmetry on compact Kähler spaces
type: Item
instance of: scholarly article
title: Hodge spectral sequence and symmetry on compact Kähler spaces
zbMATH Open document ID: 0635.32008
author: Takeo Ohsawa
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1987-01-01T00:00:00Z
review text: Let X be a compact Kähler space of pure dimension, and \(Y\subset X\) a complex subspace such that (X\(\setminus Y)\) is smooth. It is proved that the Hodge spectral sequence on (X\(\setminus Y)\) degenerates at its \(E_ 1\)-term \((:=Ker {\bar \partial}/Im {\bar \partial})\) in degrees less than \(((co\dim Y)-1);\) moreover, if \(p+q\leq ((co\dim Y)-2)\) then: \(E_ 1^{p,q}(X\setminus Y)\cong E_ 1^{q,p}(X\setminus Y).\) The proof uses an L 2-version of Andreotti-Grauert's vanishing theorem on q-complete spaces, as well as Andreotti-Vesentini's theorem.
Mathematics Subject Classification ID: 32C35
Mathematics Subject Classification ID: 32J25
Mathematics Subject Classification ID: 32F10
Mathematics Subject Classification ID: 53B35
zbMATH DE Number: 4034108
zbMATH Keywords: Hodge relations
zbMATH Keywords: singular Kähler spaces
zbMATH Keywords: q-completeness
reviewed by: Frédéric Campana
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195176250
OpenAlex ID: W2073430623
cites work: Théorèmes de finitude pour la cohomologie des espaces complexes
cites work: Carleman estimates for the Laplace-Beltrami equation on complex manifolds
cites work: Q5814415
cites work: Isomorphism theorems for cohomology groups of weakly 1-complete manifolds
cites work: Cohomology vanishing theorems on weakly 1-complete manifolds
cites work: Hodge spectral sequence on compact Kähler spaces
cites work: Hodge spectral sequence on pseudoconvex domains
cites work: Q5677789
DOI: 10.2977/PRIMS/1195176250
description: scientific article; zbMATH DE number 4034108