$$L^2$$ -Serre Duality on Singular Complex Spaces and Applications

DOI10.1007/978-4-431-55744-9_23zbMath1350.32035arXiv1409.1382OpenAlexW2307904218MaRDI QIDQ3448919

Jean Ruppenthal

Publication date: 27 October 2015

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.1382

zbMATH Keywords

Dolbeault cohomologyCauchy-Riemann equationsrational singularitiesvanishing theoremsSerre dualitysingular complex spaces\(L^2\)-theory

Mathematics Subject Classification ID

Analytic sheaves and cohomology groups (32C35) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) Transcendental methods of algebraic geometry (complex-analytic aspects) (32J25) Duality theorems for analytic spaces (32C37) Local cohomology of analytic spaces (32C36)

Related Items (1)

Koppelman formulas on the \(A_{1}\)-singularity

Cites Work

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• Explicit Serre duality on complex spaces
• \(L^2\)-theory for the \(\overline{\partial}\)-operator on compact complex spaces
• On the extension of \(L^ 2\) holomorphic functions
• Un théorème de dualité
• Cheeger-Goreski-MacPherson's conjecture for the varieties with isolated singularities
• The \({\overline{\partial}}\)-equation on homogeneous varieties with an isolated singularity
• Relative vanishing theorems in analytic spaces
• Invariance of plurigenera
• Grothendieck duality and base change
• Analyticity of sets associated to Lelong numbers and the extension of closed positive currents
• A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas
• \(L ^{2}\)-\(\overline{\partial}\)-cohomology groups of some singular complex spaces
• Carleman estimates for the Laplace-Beltrami equation on complex manifolds
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen
• Complexe dualisant et théorèmes de dualité en géométrie analytique complexe
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• Théorèmes de finitude pour la cohomologie des espaces complexes
• The Hartogs extension theorem on (n – 1)-complete complex spaces
• On Hartogs' extension theorem on (n – 1)-complete complex spaces
• ABOUT THE $\bar{\partial}$-EQUATION AT ISOLATED SINGULARITIES WITH REGULAR EXCEPTIONAL SET
• $L^2 - \overline \partial$-Cohomology of Complex Projective Varieties
• Singularities of Pairs
• LOCAL L² RESULTS FOR $\bar\partial$: THE ISOLATED SINGULARITIES CASE
• Solving on product singularities
• $L^2$ -Serre Duality on Singular Complex Spaces and Rational Singularities

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