The Dolbeault cohomology group 
of a complex
manifold 
is the quotient of 
-closed
smooth 
-forms by 
-exact forms.
The Dolbeault theorem identifies it with the sheaf cohomology of holomorphic 
-forms.
Dolbeault Cohomology
See also
Complex Manifold, Del Bar Operator, Differential k-Form, Hodge TheoryExplore with Wolfram|Alpha
References
Wells, R. O. Jr. Differential Analysis on Complex Manifolds, 3rd ed. New York: Springer-Verlag, 2008.Cite this as:
Weisstein, Eric W. "Dolbeault Cohomology." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DolbeaultCohomology.html