The Dolbeault complex with weights according to normal crossings

DOI10.1007/s00209-008-0424-4zbMath1189.32019arXiv0803.1187OpenAlexW1996214053MaRDI QIDQ841107

Jean Ruppenthal

Publication date: 14 September 2009

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.1187

zbMATH Keywords

Dolbeault complexintegral operatorsCauchy-Riemann equations

Mathematics Subject Classification ID

Modifications; resolution of singularities (complex-analytic aspects) (32S45) Analytic sheaves and cohomology groups (32C35) Holomorphic functions of several complex variables (32A10) Local cohomology of analytic spaces (32C36)

Related Items

The \({\overline{\partial}}\)-equation on homogeneous varieties with an isolated singularity ⋮ An L2-Poincaré–Dolbeault lemma of spaces with mixed cone-cusp singular metrics

Cites Work

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• Cheeger-Goreski-MacPherson's conjecture for the varieties with isolated singularities
• A \(\overline{\partial}\)-theoretical proof of Hartogs' extension theorem on Stein spaces with isolated singularities
• Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
• Pure Hodge structure on the L2 -cohomology of varieties with isolated singularities
• $L^2 - \overline \partial$-Cohomology of Complex Projective Varieties
• Local $L^2$ results for $\overline{\partial}$ on a singular surface
• Semiglobal results for $\overline \partial $ on a complex space with arbitrary singularities
• LOCAL L² RESULTS FOR $\bar\partial$: THE ISOLATED SINGULARITIES CASE
• The Hironaka theorem on resolution of singularities (Or: A proof we always wanted to understand)

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