Let $f:X \rightarrow Y$, be a proper birational morphism of projective algebraic varieties with $X$ smooth. Denote by $R^if_* \mathcal{O}_X$, the higher direct image sheaves.
Do exists a simple way to compute the sections of such sheaves?
I want to know if the inequality $ h^0( X, R^1 f_* \mathcal{O}_X) \leq h^1(X, \mathcal{O}_X) $ holds in general.