Timeline for Relatively ample line bundles
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 10, 2017 at 19:36 | comment | added | Li Yutong | @BCnrd Do you mean EGA $III_1$, 4.7.1 in Chapter III page 434? But I am not able to find the result you referred to... | |
| Jun 13, 2010 at 15:47 | vote | accept | Roman Fedorov | ||
| Jun 13, 2010 at 10:35 | answer | added | Olivier Benoist | timeline score: 3 | |
| Jun 13, 2010 at 9:02 | answer | added | Gianni Bello | timeline score: 5 | |
| Jun 12, 2010 at 22:49 | comment | added | Henri | If the morphism is projective, you can see this using the relative Kleiman's criterion. | |
| Jun 12, 2010 at 22:35 | comment | added | BCnrd | Probably you want the morphism in question to be proper, and also finitely presented (if no noetherian hypotheses). If so, then one can say a bit more: the locus of points in the base for which the line bundle is ample on fibers is open, and over that open in the base it is relatively ample. See EGA IV$_3$, 9.6.4. If you insist on assuming the base scheme is locally noetherian then simpler proofs of these can be found in EGA III$_1$, 4.7.1. Could also ask if true for proper morphisms not assumed to be finitely presented. I have some ideas on that, but not clear (and probably nobody cares). | |
| Jun 12, 2010 at 20:49 | history | asked | Roman Fedorov | CC BY-SA 2.5 |