# Direct image of structural sheaf [closed]

Let $\pi:X\rightarrow Y$ be a double cover where $X$ and $Y$ are projective smooth curves.

Is it true that $R^1\pi_*\mathcal O_X=0$ ? Why ?

• and for all coherent sheaves $\mathscr{F}$. – Francesco Polizzi Jan 31 '15 at 12:32