Dolbeault Cohomology - Construction of The Cohomology Groups

Construction of The Cohomology Groups

Let Ωp,q be the vector bundle of complex differential forms of degree (p,q). In the article on complex forms, the Dolbeault operator is defined as a differential operator on smooth sections

Since

this operator has some associated cohomology. Specifically, define the cohomology to be the quotient space

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