Timeline for Deligne Mumford Compactification of Moduli Space Of Annuli
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Dec 2, 2020 at 12:14 | comment | added | Yaniv Ganor | I think what Mohammed meant is that if one glues the node on a singly-pinched annulus (with two marked points) the two marked points will never be diametrically opposite, which now I don't actually understand why, I have to admit. Mohammed, could you please elaborate on that? @MohammedAbouzaid | |
| Dec 1, 2020 at 15:54 | comment | added | Luigi M | @MohammedAbouzaid Sorry for commenting such an old post but I can't figure out what do you mean by "if there were only one component [...] The two marked points don't satisfy the required constraint". How do you encode in the moduli space that the two marked points must belong to different boundary components? | |
| May 18, 2017 at 17:34 | comment | added | Yaniv Ganor | Thank you, Mohammed, it all makes sense now. also thanks for the reference to Liu's thesis, exactly the kind of exposition I needed. | |
| May 18, 2017 at 17:32 | vote | accept | Yaniv Ganor | ||
| May 18, 2017 at 12:57 | comment | added | Mohammed Abouzaid | Let me note the sentence just after Equation (C.8) requires that there be two marked points at $\{1,-r\}$. These are "diametrically opposite," which is why the limit breaks up into two discs. If there was only one component, then, after gluing the node, you would find that the two marked points don't satisfy the required constraint. If there were three or more components, then one of them would not carry any marked point, and hence would be unstable. Less importantly, since you link to the arXiv version, you should probably say that it's on p. 38. | |
| May 18, 2017 at 7:41 | answer | added | user_1789 | timeline score: 4 | |
| May 18, 2017 at 5:33 | history | edited | Yaniv Ganor | CC BY-SA 3.0 |
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| May 17, 2017 at 19:26 | comment | added | user21574 | The right person to ask is Aleksey Zinger | |
| May 17, 2017 at 19:02 | history | asked | Yaniv Ganor | CC BY-SA 3.0 |