Hodge spectral sequence on pseudoconvex domains
type: Item
instance of: scholarly article
title: Hodge spectral sequence on pseudoconvex domains
zbMATH Open document ID: 0638.32016
DOI: 10.1007/BF01161626
author: Takeo Ohsawa
author: Kensho Takegoshi
published in: Mathematische Zeitschrift
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183754
review text: The authors' main result is Theorem 4.3: Let \((M,ds^ 2_ M)\) be a Kähler manifold of dimension n and let D be a relatively compact pseudoconvex domain in M with \(C^{\infty}\)-smooth boundary. Suppose that the corank of the Levi form of \(\partial D\) is \(<k\) everywhere on \(\partial D\). Then \[ H^ r(D,{\mathbb{C}})\cong \oplus_{p+q=r}H^{p,q}(D),\quad r\leq n+k;\quad H^{p,q}(D)\cong H^{q,p}(D),\quad p+q\leq n+k. \] This theorem, combined with Andreotti- Grauert's isomorphism theorem on q-convex spaces, implies the theorem of the first-named author [Invent. Math. 63, 335-354 (1981; Zbl 0457.32007)], which is analogue of Hodge's theorem on pseudoconvex manifolds.
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 32F10
Mathematics Subject Classification ID: 14F40
zbMATH DE Number: 4040293
zbMATH Keywords: q-convex Kähler manifolds
zbMATH Keywords: cohomologies on Hermitian manifolds
zbMATH Keywords: Hodge spectral sequence
zbMATH Keywords: de Rham complex
zbMATH Keywords: Dolbeault cohomology
zbMATH Keywords: pseudoconvex domain
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4040293