On Hartogs' extension theorem on (n – 1)-complete complex spaces

DOI10.1515/CRELLE.2009.089zbMath1186.32001arXiv0811.1963OpenAlexW2068901875MaRDI QIDQ3404369

Jean Ruppenthal, Mihnea Colţoiu

Publication date: 9 February 2010

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.1963

zbMATH Keywords

holomorphic extensionDolbeault cohomology\(\bar\partial\)-equationHartogs' extensionconnected normal complex cohomologically \((n-1)\)-complete spaceEhrenpreis' technique

Mathematics Subject Classification ID

Continuation of analytic objects in several complex variables (32D15) Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02)

Related Items (9)

$$L^2$$ -Serre Duality on Singular Complex Spaces and Applications ⋮ A generalization of Takegoshi's relative vanishing theorem ⋮ Hartogs extension theorems on Stein spaces ⋮ The Hartogs extension phenomenon in toric varieties ⋮ On the Hartogs extension theorem for unbounded domains in \(\mathbb{C}^n\) ⋮ Hartogs-type extension for tube-like domains in \(\mathbb C^2\) ⋮ Weighted Koppelman formulas and the \(\bar\partial\)-equation on an analytic space ⋮ Semiglobal results for $\overline∂$ on complex spaces with arbitrary singularities, Part II ⋮ On Hartogs' extension

Cites Work

• Un théorème de dualité
• Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen
• A vanishing theorem for proper direct images
• Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
• Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen
• The divisor class groups of some rings of holomorphic functions
• A new proof and an extension of Hartog’s theorem
• Flattening Theorem in Complex-Analytic Geometry
• On Serre Duality and Envelopes of Holomorphy
• The boundary problem in \(q\)-convex manifolds and the Hartogs-Bochner phenomenon

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