Timeline for Degeneration of vector bundles on an algebraic curve
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Jun 20, 2021 at 15:03 | history | bounty ended | CommunityBot | ||
| S Jun 20, 2021 at 15:03 | history | notice removed | CommunityBot | ||
| Jun 16, 2021 at 16:12 | comment | added | Alexander Braverman | Actually, I think I proved it in the case when $\mathcal E$ is very stable, which is what I needed in the first place. But I don't know if it is true for stable bundles (I don't understand what you mean by taking limit here). | |
| Jun 15, 2021 at 13:17 | comment | added | Evgeny Shinder | Actually, I think if you assume the statement for stable $\mathcal{E}$, then the one for general $\mathcal{E}$ may follow by the following induction argument: consider the HN filtration on $\mathcal{E}$, and take its limit to the special fiber. | |
| Jun 14, 2021 at 19:20 | comment | added | Evgeny Shinder | If you restrict to only semistable bundles, then points of the coarse moduli space are S-equivalence classes which is kind of a filtration like you ask? | |
| Jun 14, 2021 at 14:13 | comment | added | Mohan | It is possible to construct a family with general member trivial (direct sum of the structure sheaf) and special member indecomposable. | |
| Jun 14, 2021 at 13:42 | comment | added | Alexander Braverman | Yes, but frankly I don't think it should be true for arbitrary $\mathcal E$. But I do believe that it should be true if you impose some stability requirements on $\mathcal E$ (I certainly think that it should be true for very stable bundles, maybe also for just stable ones). | |
| Jun 14, 2021 at 2:33 | comment | added | Mohan | Just so that I understand. If you had a family of vector bundles, say of rank 2, with all isomorphic for $t\neq 0$ and at zero it is indecomposable, you want the special member isomorphic to the general? If false, will it give you an example for question 1? | |
| S Jun 12, 2021 at 12:33 | history | bounty started | Alexander Braverman | ||
| S Jun 12, 2021 at 12:33 | history | notice added | Alexander Braverman | Draw attention | |
| Jun 11, 2021 at 14:06 | answer | added | Angelo | timeline score: 1 | |
| Jun 7, 2021 at 16:51 | answer | added | Mohan | timeline score: 3 | |
| Jun 7, 2021 at 13:32 | history | asked | Alexander Braverman | CC BY-SA 4.0 |