\(L ^{2}\)-\(\overline{\partial}\)-cohomology groups of some singular complex spaces

DOI10.1007/s00222-012-0414-3zbMath1279.32007arXiv1101.1860OpenAlexW2469037646MaRDI QIDQ2377346

Nils Øvrelid, Sophia K. Vassiliadou

Publication date: 28 June 2013

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.1860

zbMATH Keywords

resolution of singularitiesisolated singularities\(\overline\partial\)-operatorsingular complex spaces\(L^2\)-theory

Mathematics Subject Classification ID

Germs of analytic sets, local parametrization (32B10) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Transcendental methods of algebraic geometry (complex-analytic aspects) (32J25) Local cohomology of analytic spaces (32C36)

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Cites Work

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• \(L^2\)-theory for the \(\overline{\partial}\)-operator on compact complex spaces
• \(L^ 2\)-cohomology of normal algebraic surfaces. I
• Hartogs extension theorems on Stein spaces
• On Segre products and applications
• Cycle maximal et invariant d'Euler local des singularités isolées de surfaces
• On weakly rational singularities in complex analytic geometry
• The \({\overline{\partial}}\)-equation on homogeneous varieties with an isolated singularity
• Relative vanishing theorems in analytic spaces
• Local cohomology along exceptional sets
• Relative vanishing theorems. I: Applications to ample divisors
• On rational singularities in dimensions \(>2\)
• The \(L_ 2-{\bar \partial}\)-cohomology of an algebraic surface
• Remarks on the \(L^ 2\)-cohomology of singular algebraic surfaces
• Higher direct images of canonical sheaves tensorized with semi-positive vector bundles by proper Kähler morphisms
• \(L ^{2}\)-\(\overline{\partial}\)-cohomology groups of some singular complex spaces
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• On the extension of holomorphic functions from the boundary of a complex manifold
• Über Modifikationen und exzeptionelle analytische Mengen
• Analytic sheaf cohomology groups of dimension n of \(n\)-dimensional noncompact complex manifolds
• Pure Hodge structure on the L2 -cohomology of varieties with isolated singularities
• $L^{2}$ Serre duality on domains in complex manifolds and applications
• L 2 -Cohomology, Nash Blowup, and Semismall Resolutions
• Théorèmes de finitude pour la cohomologie des espaces complexes
• Some <i>L</i><sup xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> results for $\overline\partial$ on projective varieties with general singularities
• ABOUT THE $\bar{\partial}$-EQUATION AT ISOLATED SINGULARITIES WITH REGULAR EXCEPTIONAL SET
• $L^2 - \overline \partial$-Cohomology of Complex Projective Varieties
• Semiglobal results for $\overline \partial $ on a complex space with arbitrary singularities
• LOCAL L² RESULTS FOR $\bar\partial$: THE ISOLATED SINGULARITIES CASE
• <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup></mml:math>-theory for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>∂</mml:mi> <mml:mo>¯</mml:mo></mml:mover></mml:math>-operator on complex spaces with isolated singularities
• Normal Two-Dimensional Singularities. (AM-71)
• On Rational Singuarities
• The Nash sheaf of a complete resolution

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