What is the best reference in English for the following theorem of Grauert–Riemenschneider:
Theorem:
Let $\phi:X \to Y$ be a proper bi-rational morphism of algebraic varieties over characteristic $0$ field. Assume that $X$ is smooth. Let $\Omega_X$ be the sheaf of top differential forms on $X$.Then $R\phi_*(\Omega_X)=\phi_*(\Omega_X)$, i.e. $H^i(R\phi_*(\Omega_X))=0$ for all $i \neq 0$.
I found the original Grauert–Riemenschneider:
but I can't read German, and the review does not state this formulation of the theorem (it probably states a more general one, but I do not understand it and do not see how to deduce what I need)
Thank you
Best Answer
Dear Rami,
You could see Kollar-Mori, Birational geometry of algebraic varieties. (Page 73)
or
Lazarsfeld, Positivity in Algebraic Geometry I and II. (Page 257)