I have a question about a step in following proof gived in Badescu's "Algebraic Surfaces":
I the given setting by assumption the ideal sheaf $I$ is finitely generated therefore there exist following short ex sequence of sheaves:
$$0 \to K \to O_X^m \to I \to O$$
with $K$ kernel of right map.
My question why the second sheaf cohomology group $H^2(K)$ vanish?