The Stacks project

Lemma 108.7.1. The diagonal of $\mathrm{Hilb}_{X/B} \to B$ is a closed immersion of finite presentation.

Proof. In Quot, Lemma 99.9.2 we have seen that $\mathrm{Hilb}_{X/B} = \mathrm{Quot}_{\mathcal{O}_ X/X/B}$. Hence this follows from Lemma 108.5.1. $\square$

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