Timeline for Vanishing of the top Chern class of a vector bundle
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 11, 2015 at 12:07 | comment | added | Arne Smeets | Yes, I meant a holomorphic section (which may not exist, indeed). | |
| Feb 11, 2015 at 10:42 | comment | added | Sasha | If $F$ is globally generated then $c_{top}(F) = 0$ if and only if the zero locus of a generic section of $F$ is empty. Otherwise this is not necessarily true. Take for example $X = P^1\times P^1$ and $F = O(-1,0) \oplus O(1,0)$. Its top Chern class vanishes, but its generic section has nonempty zero locus. | |
| Feb 11, 2015 at 10:27 | comment | added | abx | I think the OP is talking about holomorphic (= algebraic) section, which might very well not exist. | |
| Feb 11, 2015 at 10:20 | comment | added | Simon Rose | Yeah, that's correct. That was just poor phrasing on my part. | |
| Feb 11, 2015 at 10:16 | history | answered | Simon Rose | CC BY-SA 3.0 |