Hi everyone. I need the following statement:

For a Kahler manifold $X$, the natural map $H^n(X,\mathbb{C})\to H^n(X,\mathcal{O})$ (from the sheaf extension) coincides with the Hodge projection $\Pr_{0,n}$, up to the de Rham isomorphism and the Dolbeault isomorphism.

Does anybody know a good reference?

P.S. Surely there must be a reference. I am much less interested in proofs: I think I know one.