Timeline for Negative degree line bundles over a singular projective curve have no sections?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 13, 2015 at 14:31 | vote | accept | Kali | ||
| Aug 27, 2014 at 13:12 | comment | added | Roberto Pignatelli | Sorry, i misread. | |
| Aug 27, 2014 at 13:08 | comment | added | abx | The OP assumes that $C$ is integral, so I answered in this setting. Mumford has a much weaker assumption which eliminates the kind of example you give. | |
| Aug 27, 2014 at 13:00 | comment | added | Roberto Pignatelli | I do not have Mumford's book avalaible now, but it seems to me that this is not quite true. If you take two intersecting lines, you can construct on it a bundle which restricts to O(1) on a line and O(-2) on the other line. This has degree -1 and h^0=1: the non trivial section will vanish on the whole second line. Indeed on reducible curves one usually consider positive bundles as bundles which have positive degree when restricted to each factor. | |
| Aug 26, 2014 at 9:19 | history | answered | abx | CC BY-SA 3.0 |