# Dimension of cohomology group is a birational invariant

I read the fact somewhere that the dimension of cohomology group $H^i(X,\mathcal{O}_X)$ is a birational invariant.

For surfaces, the reference for this fact is Hartshorne Proposition 3.4 saying $H^i(X, \mathcal{O}_X) \cong H^i(\tilde{X}, \mathcal{O}_{\tilde{X}})$ for all $i \geq 0$ where $\tilde{X}$ is a blow-up of $X$ at $1$ point, combined with the fact that any birational morphism between surfaces factors as a finite number of blow-ups (of a point) and an isomorphism (Beauville-Complex Algebraic Surfaces, Theorem II.11).

What is the source for varieties of higher dimensions?