Timeline for does a line bundle always have a degree
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 5, 2023 at 13:46 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Math Jaxed
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| Oct 12, 2009 at 23:40 | vote | accept | solbap | ||
| Oct 12, 2009 at 23:40 | |||||
| Oct 12, 2009 at 22:04 | comment | added | S. Carnahan♦ | Yeah, see Lemma 1.2 and its proof in section 4.1 in Hartshorne. Your divisor has to be effective to get h^0 positive, and if it has degree 0, then it is the zero divisor. I believe this extends to all proper varieties. | |
| Oct 12, 2009 at 6:09 | comment | added | solbap | I see, so maybe I mean to ask a much harder question. For nonsingular curves over C I think its true that degree(L) = 0 plus h^0(L) = 1 implies that L = O_X. So I guess I'm wondering how many assumptions you can relax (if any) before this stops being true. | |
| Oct 11, 2009 at 6:45 | history | answered | S. Carnahan♦ | CC BY-SA 2.5 |