ABOUT THE $\bar{\partial}$-EQUATION AT ISOLATED SINGULARITIES WITH REGULAR EXCEPTIONAL SET

DOI10.1142/S0129167X09005388zbMath1180.32015MaRDI QIDQ3632273

Jean Ruppenthal

Publication date: 23 June 2009

Published in: International Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

\(L^2\)-estimates\(\overline\partial\)-equation

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) Local cohomology of analytic spaces (32C36)

Related Items (12)

<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 ⋮ $$L^2$$ -Serre Duality on Singular Complex Spaces and Applications ⋮ The \({\overline{\partial}}\)-equation on homogeneous varieties with an isolated singularity ⋮ Some applications of metric currents to complex analysis ⋮ \(L ^{2}\)-\(\overline{\partial}\)-cohomology groups of some singular complex spaces ⋮ On Wirtinger derivations, the adjoint of the operator $\overline\partial$, and applications ⋮ An explicit \(\bar {\partial }\)-integration formula for weighted homogeneous varieties. II: Forms of higher degree ⋮ Subelliptic estimates for the \(\bar\partial\)-problem on a singular complex space ⋮ \(L^2\)-theory for the \(\overline{\partial}\)-operator on compact complex spaces ⋮ Compactness of the \(\bar{\partial}\)-Neumann operator on singular complex spaces ⋮ \(L^2\)-properties of the \(\overline{\partial}\) and the \(\overline{\partial}\)-Neumann operator on spaces with isolated singularities ⋮ An explicit \(\overline {\partial}\)-integration formula for weighted homogeneous varieties

Cites Work

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• Strongly plurisubharmonic exhaustion functions on 1-convex spaces
• Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
• The Cauchy Riemann equation on singular spaces.
• On the equivalence of imbeddings of exceptional complex spaces
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• Über Modifikationen und exzeptionelle analytische Mengen
• Analytic sheaf cohomology groups of dimension n of \(n\)-dimensional noncompact complex manifolds
• Riemannsche Hebbarkeitssätze für Cohomologieklassen
• Eine Anwendung Riemannscher Hebbarkeitssätze für analytische Cohomologieklassen
• 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)
• Solving on product singularities

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