Hodge structure and holonomic systems
type: Item
instance of: scholarly article
title: Hodge structure and holonomic systems
zbMATH Open document ID: 0629.14006
author: Takahiro Kawai
author: Masaki Kashiwara
published in: Proceedings of the Japan Academy. Series A
publication date: 1986-01-01T00:00:00Z
review text: Let X be a compact complex variety of type C in the sense of Fujiki, and \(X_ 0\) a non-singular Zariski open subset of X. Let \((H_ Z,F)\) be a variation of Hodge structure on \(X_ 0\) of weight w. The well-known conjecture is that the cohomology group \(H^ n(X;^{\pi}H_ Q)\) has a Hodge structure of weight \(n+w.\) Toward this direction, we gave the affirmative answer in Proc. Japan Acad., Ser. A 61, 164-167 (1985; Zbl 0576.14010; see also the preceding review) when X is a non-singular Kähler manifold and \(S=X\setminus X_ 0\) is a normally crossing hypersurface. It was also given by \textit{E. Cattani}, \textit{A. Kaplan} and \textit{W. Schmidt} [Invent. Math. 87, 217-252 (1987; Zbl 0611.14006)] independently. But, the Hodge filtration of the cohomology groups was not given in an algebro-geometric way. In this article we announce how to construct the Hodge filtration in an algebraic way.
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 32J25
zbMATH DE Number: 4023449
zbMATH Keywords: compact complex variety of type C
zbMATH Keywords: Hodge filtration of the cohomology groups
MaRDI profile type: Publication
full work available at URL: pjaa.62.1
OpenAlex ID: W2051000671
cites work: Q3693615
cites work: \(L^ 2\) and intersection cohomologies for a polarizable variation of Hodge structure
cites work: Closedness of the Douady spaces of compact Kähler spaces
cites work: The Poincaré lemma for a variation of polarized Hodge structure
cites work: Q5566770
cites work: Variation of Hodge structure: The singularities of the period mapping
cites work: Hodge theory with degenerating coefficients: \(L_2\) cohomology in the Poincaré metric
DOI: 10.3792/PJAA.62.1
description: scientific article; zbMATH DE number 4023449