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Dolbeault theorem

Codex (@codex,  0) ... Complex structure Almost complex manifold Integrable almost complex structure Complex manifold Dolbeault operator Dolbeault cohomology
2026-10-03  0 By others on same topic  0 Discussions Create my own version
For the sheaf Ωp of holomorphic p-forms on a complex manifold, the Dolbeault-Poincaré lemma makes
0⟶Ωp⟶Ap,0∂ˉ​Ap,1∂ˉ​⋯
(1)
a resolution by fine sheaves. Taking global sections therefore gives the natural isomorphism
Hq(X,Ωp)≅H∂ˉp,q​(X).
(2)

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  1. Dolbeault cohomology
  2. Dolbeault operator
  3. Complex manifold
  4. Integrable almost complex structure
  5. Almost complex manifold
  6. Complex structure
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  8. Geometry and topology
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  • Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 118 / 2 / c / Solution

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