Lemma 31.32.13. Let $X$ be a scheme. Let $\mathcal{I} \subset \mathcal{O}_ X$ be a quasi-coherent sheaf of ideals. Let $b : X' \to X$ be the blowing up of $X$ in the ideal sheaf $\mathcal{I}$. If $\mathcal{I}$ is of finite type, then

$b : X' \to X$ is a projective morphism, and

$\mathcal{O}_{X'}(1)$ is a $b$-relatively ample invertible sheaf.

## Comments (0)

There are also: