Hodge theory and holomorphic De Rham complexes for certain analytic spaces. I.
type: Item
instance of: scholarly article
title: Hodge theory and holomorphic De Rham complexes for certain analytic spaces. I.
zbMATH Open document ID: 0928.32004
DOI: 10.1016/S0007-4497(98)80087-0
author: Vincenczo Ancona
author: Bernard Gaveau
published in: Bulletin des Sciences Mathématiques
publication date: 2000-01-09T00:00:00Z
review text: For a complex analytic space with a smooth singular locus and a smooth exceptional divisor, the following constructions are given: a sequence of de Rham complexes, Hodge filtrations with associated spectral sequences, holomorphic de Rham complexes with the usual properties in Hodge theory. Specifically, (i) for every natural number \(r\), a fine de Rham complex of differential forms is constructed, with a type definition for the forms; (ii) the associated spectral sequence converges to the graded de Rham cohomology; (iii) for every \(r\), a holomorphic de Rham complex is defined whose cohomology is the first term of the mentioned spectral sequence; (iv) for sufficiently great \(r\), the graded de Rham cohomology does not depend on \(r\). Remark: There is the question of defining the analog of harmonic forms, i.e. is it possible to define canonical representatives in the cohomology classes of the considered analytic spaces?
reviewed by: Alfred Aeppli
Mathematics Subject Classification ID: 32C15
Mathematics Subject Classification ID: 32C35
zbMATH DE Number: 1160374
zbMATH Keywords: Hodge theory
zbMATH Keywords: complex analytic space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1160374