An explicit \(\overline {\partial}\)-integration formula for weighted homogeneous varieties

DOI10.1307/mmj/1250169071zbMath1214.32017OpenAlexW2161773953MaRDI QIDQ1045738

Jean Ruppenthal, Eduardo S. Zeron

Publication date: 15 December 2009

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1307/mmj/1250169071

Mathematics Subject Classification ID

Complex spaces (32C15) Differential operators in several variables (32W99)

Related Items

The \({\overline{\partial}}\)-equation on homogeneous varieties with an isolated singularity ⋮ 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 ⋮ 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 ⋮ Koppelman formulas on the \(A_{1}\)-singularity ⋮ Global Koppelman formulas on (singular) projective varieties

Cites Work

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• The \({\overline{\partial}}\)-equation on homogeneous varieties with an isolated singularity
• Hölder estimates for the \(\overline\partial\)-equation on surfaces with singularities of the type \(E_6\) and \(E_7\)
• Singularities and topology of hypersurfaces
• Hölder estimates for the \(\overline\partial\)-equation in some domains of finite type
• The Cauchy Riemann equation on singular spaces.
• Hölder estimates for the \(\overline \partial\)-equation on surfaces with simple singularities
• Riemannsche Hebbarkeitssätze für Cohomologieklassen
• ABOUT THE $\bar{\partial}$-EQUATION AT ISOLATED SINGULARITIES WITH REGULAR EXCEPTIONAL SET
• 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
• Solving on product singularities