A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas

DOI10.1007/s00222-012-0380-9zbMath1271.32009arXiv1010.6142OpenAlexW2081976797WikidataQ124819476 ScholiaQ124819476MaRDI QIDQ1930892

Mats Andersson, Håkan Samuelsson Kalm

Publication date: 14 January 2013

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

Full work available at URL: https://arxiv.org/abs/1010.6142

zbMATH Keywords

Dolbeault complexKoppelman formulassingular complex spacesstructure sheaf\(\overline\partial\)-homotopy formulaGrothendieck-Dolbeault lemma

Mathematics Subject Classification ID

Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels) (32A26) Analytic subsets of affine space (32B15) Integration on analytic sets and spaces, currents (32C30) Residues for several complex variables (32A27)

Related Items

$$L^2$$ -Serre Duality on Singular Complex Spaces and Applications, A pointwise norm on a non-reduced analytic space, Division formulas on projective varieties, Explicit Hodge decomposition on Riemann surfaces, Direct images of semi-meromorphic currents, Explicit Serre duality on complex spaces, On the Effective Membership Problem for Polynomial Ideals, The \(\bar{\partial}\)-equation, duality, and holomorphic forms on a reduced complex space, A Briançon-Skoda-type result for a non-reduced analytic space, Estimates for the \({\bar{\partial }} \)-equation on canonical surfaces, On the duality theorem on an analytic variety, Norm estimates for the \(\bar{\partial}\)-equation on a non-reduced space, The \(\bar{\partial }\)-equation on a non-reduced analytic space, On Wirtinger derivations, the adjoint of the operator $\overline\partial$, and applications, Subelliptic estimates for the \(\bar\partial\)-problem on a singular complex space, Computing residue currents of monomial ideals using comparison formulas, The Briançon-Skoda number of analytic irreducible planar curves, A note on the singularities of residue currents of integrally closed ideals, Regularity of pseudomeromorphic currents, Weighted Koppelman formulas and the \(\bar\partial\)-equation on an analytic space, \(L^2\)-properties of the \(\overline{\partial}\) and the \(\overline{\partial}\)-Neumann operator on spaces with isolated singularities, Koppelman formulas on the \(A_{1}\)-singularity, Residue currents with prescribed annihilator ideals on singular varieties, Koppelman formulas on affine cones over smooth projective complete intersections, Integral representation of moderate cohomology, Pseudomeromorphic currents on subvarieties, Global Koppelman formulas on (singular) projective varieties, A comparison formula for residue currents, Global effective versions of the Briançon-Skoda-Huneke theorem, Explicit Hodge-type decomposition on projective complete intersections

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