The Stacks project

Lemma 70.17.8. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $b : X' \to X$ be the blowup of $X$ in a closed subspace. If $X$ satisfies the equivalent conditions of Morphisms of Spaces, Lemma 66.49.1 then so does $X'$.

Proof. Follows immediately from the lemma cited in the statement, the ├ętale local description of blowing ups in Lemma 70.17.2, and Divisors, Lemma 31.32.10. $\square$


Comments (2)

Comment #4311 by Ziyu Zhang on

There might be a typo in the third sentence of the statement: I think "is" should be "in".

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  • 2 comment(s) on Section 70.17: Blowing up

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