Extendability of differential forms on non-isolated singularities
type: Item
instance of: scholarly article
title: Extendability of differential forms on non-isolated singularities
zbMATH Open document ID: 0658.14009
DOI: 10.1007/BF01394328
author: Hubert Flenner
published in: Inventiones Mathematicae
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143629
review text: In these decades Hodge theory has been extended to the germs of isolated singular points of complex spaces by several people, and continuation theorems for holomorphic differential forms across exceptional sets have been known as application. This article first gives a nice survey on this topic, collecting the results obtained by \textit{D. v. Straten} and \textit{J. Steenbrink} [Abh. Math. Semin. Univ. Hamburg 55, 97-109 (1985; Zbl 0584.32018)'), \textit{V. Navarro Aznar} [Systèmes différentiels et singularités, Colloq. Luminý, Astérisque 130, 272-307 (1985; Zbl 0599.14007)], \textit{Kersken} (Habilitationsschrift, Bochum 1987) and the reviewer [Publ. Res. Inst. Math. Sci. 24, No.2, 253-263 (1988; Zbl 0653.32012)], and extend them to the germs of non-isolated singular points. The result has an immediate application to the well known problem of Zariski and Lipman, as the author remarks in the introduction. The idea of the proof is very natural, but the reader is required to be acquaintd with basic techniques in algebraic geometry.
Mathematics Subject Classification ID: 14E15
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 32D15
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 32B10
Mathematics Subject Classification ID: 32S45
zbMATH DE Number: 4075258
zbMATH Keywords: Hodge theory
zbMATH Keywords: continuation theorems for holomorphic differential forms
zbMATH Keywords: germs of non-isolated singular points
MaRDI profile type: Publication
cites work: Algebraic approximation of structures over complete local rings
cites work: Die Sätze von Bertini für lokale Ringe
cites work: The Zariski-Lipman conjecture in the graded case
cites work: Q4692395
cites work: Free Derivation Modules on Algebraic Varieties
cites work: A reduction theorem for cohomology groups of very strongly q-convex Kähler manifolds
cites work: Addendum to: A reduction theorem for cohomology groups of very strongly q-convex Kaehler manifolds
cites work: Differentielle Eigenschaften der Invarianten regulärer Algebren
cites work: Q3705705
cites work: Extendability of holomorphic differential forms near isolated hypersurface singularities
description: scientific article; zbMATH DE number 4075258