The Stacks project

108.1 Introduction

In this chapter we verify basic properties of moduli spaces and moduli stacks such as $\mathit{Hom}$, $\mathit{Isom}$, $\mathcal{C}\! \mathit{oh}_{X/B}$, $\mathrm{Quot}_{\mathcal{F}/X/B}$, $\mathrm{Hilb}_{X/B}$, $\mathcal{P}\! \mathit{ic}_{X/B}$, $\mathrm{Pic}_{X/B}$, $\mathit{Mor}_ B(Z, X)$, $\mathcal{S}\! \mathit{paces}'_{fp, flat, proper}$, $\mathcal{P}\! \mathit{olarized}$, and $\mathcal{C}\! \mathit{omplexes}_{X/B}$. We have already shown these algebraic spaces or algebraic stacks under suitable hypotheses, see Quot, Sections 99.3, 99.4, 99.5, 99.6, 99.8, 99.9, 99.10, 99.11, 99.12, 99.13, 99.14, and 99.16. The stack of curves, denoted $\textit{Curves}$ and introduced in Quot, Section 99.15, is discussed in the chapter on moduli of curves, see Moduli of Curves, Section 109.3.

In some sense this chapter is following the footsteps of Grothendieck's lectures [Gr-I], [Gr-II], [Gr-III], [Gr-IV], [Gr-V], and [Gr-VI].


Comments (0)


Post a comment

Your email address will not be published. Required fields are marked.

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).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 0DLU. Beware of the difference between the letter 'O' and the digit '0'.