ABSTRACT
This chapter explains the central results concerning the cohomology of a compact ka¨hlerian manifold M . We shall prove that there is a direct sum decomposition of the cohomology of M as
Hk (M,C) = ⊕
Hp,q(M)
where Hp,q(M) = Hq (M,ΩpM ) is the ∂¯-cohomology of (p, 0)-forms. This decomposition goes much beyond mere formalities. It means that if [ϕ] is a d-cohomology class of degree k, one can find in this class a representative ϕˆ such that its decomposition in types ϕˆ =
∑ p+q=k ϕˆ
(p,q) has the property that each component ϕˆ(p,q) is d-closed and ∂¯-closed.
