Lemma 108.7.1 (0DM6)—The Stacks project

Processing math: 100%

Table of contents
Part 8: Topics in Moduli Theory
Chapter 108: Moduli Stacks
Section 108.7: Properties of the Hilbert functor
Lemma 108.7.1 (cite)

next lemma

numberstags

history
statistics
2 tags refer to this tag

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. $\square$

Comments (0)

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$ ). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Comments (0)

Post a comment