The Stacks project

Definition 89.5.1. Let $S$ be a scheme. Let $X$ be a decent algebraic space over $S$ satisfying the equivalent conditions of Morphisms of Spaces, Lemma 67.49.1. Let $x \in |X|$ be a closed point. The normalized blowup of $X$ at $x$ is the composition $X'' \to X' \to X$ where $X' \to X$ is the blowup of $X$ at $x$ (Definition 89.4.1) and $X'' \to X'$ is the normalization of $X'$.