Timeline for Stable extensions by line bundles on Riemann surfaces
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 25, 2018 at 3:04 | vote | accept | swalker | ||
| Nov 21, 2018 at 6:32 | comment | added | abx | Yes, I think that quite generally the subvariety of unstable extensions has high codimension. You might have a look at a paper by A. Bertram, Moduli of rank-2 vector bundles, theta divisors, and the geometry of curves in projective space (J. Differential Geom. 35 (1992), no. 2, 429-469). He does a detailed analysis (in a slightly different situation) of the stability of extensions. | |
| Nov 21, 2018 at 2:37 | vote | accept | swalker | ||
| Nov 25, 2018 at 3:04 | |||||
| Nov 18, 2018 at 2:48 | comment | added | swalker | If $X$ is a Riemann surface of genus $g>1$, I proved that there always exist stable extension bundles.@abx | |
| Nov 18, 2018 at 2:44 | comment | added | swalker | Thank you very much! By the openness of stability, we know that the unstable extensions form a subvariety of Ext$^1(L^{-1},L)$ of codimension $\ge 1$. Can we expect that the subvariety has codimension $>1$ for some general Riemann surfaces? For example $g(X) > 1$. | |
| Nov 17, 2018 at 9:58 | history | answered | abx | CC BY-SA 4.0 |