Lemma 31.32.8. Let $X$ be a scheme. Let $\mathcal{I} \subset \mathcal{O}_ X$ be a quasi-coherent sheaf of ideals. If $X$ is reduced, then the blowup $X'$ of $X$ in $\mathcal{I}$ is reduced.
Lemma 31.32.8. Let $X$ be a scheme. Let $\mathcal{I} \subset \mathcal{O}_ X$ be a quasi-coherent sheaf of ideals. If $X$ is reduced, then the blowup $X'$ of $X$ in $\mathcal{I}$ is reduced.
Proof. Combine Lemma 31.32.2 with Algebra, Lemma 10.70.9. $\square$
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