Timeline for Coarse moduli spaces of stacks for which every atlas is a scheme
Current License: CC BY-SA 4.0
9 events
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| Jan 15, 2022 at 22:49 | comment | added | Dori Bejleri | Yes it looks like the example from Corollary 6 does the job! After taking a quick look at the proof, it seems like the condition that the coarse space is a scheme should be equivalent to something like the following: for each point $x \in P$, there exists a linearized ample line bundle $L$ such that $x$ is $L$-semistable. I'm not sure how this interacts with your atlas condition though. | |
| Jan 15, 2022 at 18:51 | comment | added | Ariyan Javanpeykar | @DoriBejleri I think (but I'd have to double-check) that Kollar's paper arxiv.org/pdf/math/0501294.pdf contains such examples. Do you agree? (BTW, this question is seven years old, and I somehow decided to revive it now, but I don't even remember the "application in mind" at the moment.) | |
| Jan 15, 2022 at 18:28 | comment | added | Dori Bejleri | Do you have an example, without assuming your condition on the atlases, where $P$ is quasi-projective and $G$ is reductive, $[P/G]$ is separated DM, but the coarse space of $[P/G]$ is not a scheme? | |
| Jan 14, 2022 at 19:56 | history | edited | Ariyan Javanpeykar | CC BY-SA 4.0 |
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| Nov 11, 2014 at 14:12 | history | edited | Ariyan Javanpeykar | CC BY-SA 3.0 |
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| Nov 10, 2014 at 12:32 | history | edited | Ariyan Javanpeykar | CC BY-SA 3.0 |
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| Nov 9, 2014 at 14:32 | history | edited | Ariyan Javanpeykar | CC BY-SA 3.0 |
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| Nov 7, 2014 at 15:19 | history | edited | Ariyan Javanpeykar | CC BY-SA 3.0 |
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| Nov 6, 2014 at 16:42 | history | asked | Ariyan Javanpeykar | CC BY-SA 3.0 |