Timeline for Families of ideal sheaves: What's the correct definition?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
|
|
| Oct 5, 2012 at 2:10 | comment | added | Yuhao Huang | Rank one and non-zero ==> generic isomorphism, and torsion-free ==> injective (The kernel is supported on a proper closed subset, thus torsion.) | |
| Sep 19, 2012 at 17:06 | comment | added | 36min | Thanks for pointing that out. I think rank one is also part of the definition. That's specified by the numerical class. | |
| Sep 19, 2012 at 12:34 | comment | added | MartinG | I just had a look at the paper: Maybe this is also stated more explicitly elsewhere, but I think at least the proof of Lemma 6.3 reveals that an ideal sheaf means a torsion free sheaf for which there exists a nonzero map to $\mathcal{O}_X$, that for families, this condition is just imposed fibrewise (as Sasha suggested) and moreover that this is a closed condition. Anyway, I am leaving my answer as it is, covering the smooth case. (And I still have no idea whether the natural map could fail to be an iso in the singular case.) | |
| Sep 19, 2012 at 6:39 | history | edited | 36min | CC BY-SA 3.0 |
Updated the question, hopefully it makes more sense now.
|
| Sep 19, 2012 at 6:09 | answer | added | Sasha | timeline score: 2 | |
| Sep 18, 2012 at 17:04 | answer | added | MartinG | timeline score: 10 | |
| Sep 18, 2012 at 7:58 | answer | added | Sándor Kovács | timeline score: 8 | |
| Sep 18, 2012 at 6:46 | history | asked | 36min | CC BY-SA 3.0 |