Contents

complex geometry

cohomology

# Contents

## Idea

The complex geometry-analog of the de Rham theorem is the Dolbeault theorem:

For $X$ a complex manifold then its Dolbeault cohomology in bi-degree $(p,q)$ is naturally isomorphic to the abelian sheaf cohomology in degree $q$ of the abelian sheaf $\Omega^p \coloneqq \Omega^{p,0}$ of holomorphic p-forms

$H^{p,q}(X)\simeq H^q(X,\Omega^p) \,.$

## References

Review includes

• Zachary Maddock, Dolbeault cohomology (pdf)

Last revised on July 1, 2016 at 03:28:56. See the history of this page for a list of all contributions to it.