Timeline for Easiest way to see Theorem 1.2 of Deligne-Mumford's "The irreducibility of the space of curves of given genus"?
Current License: CC BY-SA 3.0
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| S Aug 30, 2015 at 5:08 | history | bounty ended | CommunityBot | ||
| S Aug 30, 2015 at 5:08 | history | notice removed | CommunityBot | ||
| S Aug 22, 2015 at 3:20 | history | bounty started | CommunityBot | ||
| S Aug 22, 2015 at 3:20 | history | notice added | user64615 | Authoritative reference needed | |
| Aug 21, 2015 at 13:54 | comment | added | Jason Starr | I want to second the comment of potentially dense: what do you mean by "easiest"? You can form the normalization $\widetilde{C}$ of $C$, you can pullback $\omega_{C/k}$ to $\widetilde{C}$, twist by an invertible ideal sheaf, pushforward to $C$, and find an injection of this pushforward into $\omega_{C/k}$ if the ideal sheaf is appropriately chosen. Is that what you are looking for? | |
| Aug 19, 2015 at 14:54 | comment | added | Lazzaro Campeotti | Here is a related question: mathoverflow.net/questions/113980/…. To me, your Question 1 seems hard to answer in its current form. If I may ask, is there a specific point or points in Deligne--Mumford's proof that is unclear to you? For example, can you see how the proof would go if $C$ were smooth instead of just stable? (I am not trying to be offensive, just to help potential answerers to calibrate their explanations.) | |
| Aug 19, 2015 at 12:02 | review | First posts | |||
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| Aug 19, 2015 at 11:59 | history | asked | Geometrer | CC BY-SA 3.0 |