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Dolbeault cohomology

In mathematics, in particular in algebraic geometry and differential geometry, Dolbeault cohomology (named after Pierre Dolbeault) is an analog of de Rham cohomology for complex manifolds. Let M be a complex manifold. Then the Dolbeault cohomology groups H p , q ( M , C ) {\displaystyle H^{p,q}(M,\mathbb {C} )} depend on a pair of integers p and q and…

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Dolbeault–Grothendieck lemma

Poincaré lemmaCauchy integral representation for smooth functionsComplex planeGrothendieckPolydisc
7 related topics

Dolbeault cohomology of vector bundles

Dolbeault operatorResolutionSheafSheaf cohomologyLeibniz rule
6 related topics

Construction of the cohomology groups

Vector bundleDifferential operatorCohomologyQuotient space
4 related topics

Dolbeault's theorem

De Rham's theoremLogarithmic formsFine sheafExact sequence
4 related topics

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Overview

Construction of the cohomology groups

Dolbeault cohomology of vector bundles

Dolbeault–Grothendieck lemma

Dolbeault's theorem

Explicit example of calculation

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Dolbeault cohomology

Nodes40
Edges39
Triples9
Avg. degree1.95
Density0.05
Components1

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Dolbeault cohomology

Top relations

related to Dolbeault's theorem · 6
Dolbeault cohomology → Dolbeault, Dolbeault's, It, Omega, Rham's, Specifically
related to Explicit example of calculation · 3
Dolbeault cohomology → Hodge, The Dolbeault, We

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Important terminology

displaystyle bar partial dolbeault varepsilon cohomology mathbb delta alpha complex lemma mathcal holomorphic open forms differential sheaf omega smooth overline

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SubjectPredicateObjectConfidenceSrc
Dolbeault cohomologyrelated to Dolbeault's theoremDolbeault's0.60section
Dolbeault cohomologyrelated to Dolbeault's theoremRham's0.60section
Dolbeault cohomologyrelated to Dolbeault's theoremIt0.60section
Dolbeault cohomologyrelated to Dolbeault's theoremDolbeault0.60section
Dolbeault cohomologyrelated to Dolbeault's theoremSpecifically0.60section
Dolbeault cohomologyrelated to Dolbeault's theoremOmega0.60section
Dolbeault cohomologyrelated to Explicit example of calculationThe Dolbeault0.60section
Dolbeault cohomologyrelated to Explicit example of calculationWe0.60section
Dolbeault cohomologyrelated to Explicit example of calculationHodge0.60section

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