Timeline for When is a coarse moduli space also a fine moduli space?
Current License: CC BY-SA 2.5
22 events
| when toggle format | what | by | license | comment | |
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| Feb 25, 2010 at 5:01 | answer | added | BCnrd | timeline score: 14 | |
| Feb 5, 2010 at 12:57 | vote | accept | Anweshi | ||
| Jan 4, 2010 at 14:46 | comment | added | Anweshi | @Ben. I have added the word "also" to the title. This should pre-empt the particular objection of yours. | |
| Jan 3, 2010 at 23:25 | comment | added | Ben Webster♦ | I didn't mean it to be rude at all. I just mean that I found it hard to guess Anweshi's level of comfort from the way the question was written. | |
| Jan 3, 2010 at 22:35 | history | edited | Anweshi | CC BY-SA 2.5 |
edited title
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| Jan 3, 2010 at 19:28 | comment | added | David Zureick-Brown | Preemptively @Pedants: I obviously mean something non trivial by the BG claim -- that the stack quotient [S/G], where G acts trivially on S, is isomorphic to the moduli stack of G-torsors. | |
| Jan 3, 2010 at 19:27 | comment | added | David Zureick-Brown | @Anweshi: One thing that helped me learn stacks was doing very basic exercises about fibered categories; once you're comfortable with the basic definitions many things (like parts of your question, or that say BG is the moduli space of G-torsors) become tautological. One source of these is the course notes from the Deformation Theory Workshop at MSRI (only some of them are note relevant): msri.org/people/members/defthy07/exercises.html | |
| Jan 3, 2010 at 16:16 | comment | added | Anweshi | @Ben. "a coarse moduli space is fine if and only if a fine moduli space exists" is annoying obvious to me since I have looked in GIT. However I am slippery with stuff like stacks. I am not experienced at that level. I am trying to figure such ideas out, and after reading the nLab page(but not any textbook on stacks or research papers), I am posing a question which seemed plausible to me. A helpful answer will enlighten me more on moduli problems and stacks. I hope my level is clear now. | |
| Jan 3, 2010 at 5:54 | comment | added | David Zureick-Brown | @Ben: Be nice; that's not genuinely helpful to anyone, and these are totally legit questions. | |
| Jan 3, 2010 at 5:42 | comment | added | Ben Webster♦ | Well, for me the issue is that I can't quite sort out what it is you really want to know, and perhaps more importantly, which facts you take for granted. For example, reading the question, I have no idea whether you would view "a coarse moduli space is fine if and only if a fine moduli space exists" as annoyingly obvious, or genuinely helpful. | |
| Jan 3, 2010 at 4:56 | history | edited | David Zureick-Brown | CC BY-SA 2.5 |
Made the title a question.
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| Jan 3, 2010 at 3:37 | comment | added | Anweshi | In fact I do not know how to make it more readable. If someone knows, please feel free to suggest, or if he/she has enough reputation, edit it himself/herself. | |
| Jan 3, 2010 at 3:34 | comment | added | Anweshi | Yes that is true. I had asked this question in 3 pieces elsewhere and failed to get an answer. When I posed it here I just glued up the pieces out of laziness, without much editing. That's why. :) | |
| Jan 3, 2010 at 3:31 | comment | added | Ben Webster♦ | Fine, fine, I guess I'm just getting cranky in my old age. I think I just found the question generally a bit hard to read, and was trying to put a finger on why. | |
| Jan 3, 2010 at 3:19 | answer | added | David Zureick-Brown | timeline score: 12 | |
| Jan 3, 2010 at 2:51 | comment | added | David Zureick-Brown | Anweshi's usage of moduli problem is standard. | |
| Jan 3, 2010 at 1:28 | answer | added | Ben Webster♦ | timeline score: 3 | |
| Jan 2, 2010 at 23:47 | history | edited | Anweshi | CC BY-SA 2.5 |
deleted 11 characters in body
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| Jan 2, 2010 at 22:51 | answer | added | Kevin Buzzard | timeline score: 5 | |
| Jan 2, 2010 at 22:41 | comment | added | Anweshi | For the definition of coarse and fine moduli spaces, I follow what is given in Mumford's Geometric Invariant Theory. A moduli problem, if you want, is the functor you are seeking to represent, in the context of definitions in that book. I suppose this book is quite standard. No?? | |
| Jan 2, 2010 at 22:08 | comment | added | Ben Webster♦ | If you really want this to be a sensible question, you had better give some kind of definition of "moduli problem." Do you just mean "sheaf on the category of rings"? | |
| Jan 2, 2010 at 21:48 | history | asked | Anweshi | CC BY-SA 2.5 |