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I am looking for examples of Deligne-Mumford stacks whose coarse moduli space is $\mathbb{A}^n$ or at least an open subscheme of $\mathbb{A}^n$ whose complement has codimension $2$. (Thus the whole interesting part of the stack lies in its stackiness.) The stacks should "come up in nature". Obvious examples are classifying stacks of etale group schemes and, more interestingly, the moduli stack of elliptic curves. Are there more examples?

Edit: I'm especially interested in stacks that naturally arise as "moduli stacks of something" (although this is, of course, not a well-defined mathematical category).

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    $\begingroup$ The quotient stack $[\mathbf{A}^n/S_n]$? ;) $\endgroup$
    – Piotr Achinger
    Commented Mar 1, 2021 at 14:42
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    $\begingroup$ More generally $[V/W]$ where $W$ is a (pseudo)-reflection group acting on $V$. By Chevalley-Shephard-Todd, these are the only examples in the world of global quotients. $\endgroup$
    – Sam Gunningham
    Commented Mar 1, 2021 at 15:10
  • $\begingroup$ @SamGunningham Do you say that every global quotient with coarse moduli space $\mathbb{A}^n$ is a quotient of $\mathbb{A}^m$? And Chevalley-Shephard-Todd only fully works in characteristic zero, right? $\endgroup$
    – Lennart Meier
    Commented Mar 1, 2021 at 19:22
  • $\begingroup$ In Sam Gunningham's example, I assume that Gunningham is considering only linear actions of finite groups on a vector space. There are many other examples that are "finite quotients" by a group that is not acting linearly on a vector space. $\endgroup$
    – Jason Starr
    Commented Mar 1, 2021 at 19:30
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    $\begingroup$ @LennartMeier yes, there are further examples in positive characteristic, such as $\mathbb{A}^n(\mathbb{F}_q) \, / \, {\rm PGL_n}(\mathbb{F}_q)$ and $\mathbb{A}^n(\mathbb{F}_q) \, / \, {\rm PSL_n}(\mathbb{F}_q)$ (Dickson invariants). $\endgroup$
    – Noam D. Elkies
    Commented Mar 1, 2021 at 19:59

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