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 ${\displaystyle H^{p,q}(M,\mathbb {C} )}$ depend on a pair of integers p and q and are realized as a subquotient of the space of complex differential forms of degree (p,q).