Timeline for Conic bundles on quartic del Pezzo surfaces
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 9, 2016 at 11:39 | vote | accept | Daniel Loughran | ||
| Aug 8, 2016 at 22:05 | answer | added | Sasha | timeline score: 5 | |
| Aug 8, 2016 at 20:11 | comment | added | Daniel Loughran | But both these conic bundles arise from pencils! And by definition, a pencil gives rise to a morphism $S \to \mathbb{P}^1$. | |
| Aug 8, 2016 at 20:10 | comment | added | Daniel Loughran | I have clarified my construction. If you have a quartic del Pezzo surface with a conic $Q$ then it in fact has 2 conics bundles. Namely you consider the pencil of hyperplanes which contain $Q$ and take the residual intersection. This gives one conic bundle. But then you can of course run this construction with the residual conics to get another conic bundle. | |
| Aug 8, 2016 at 20:08 | history | edited | Daniel Loughran | CC BY-SA 3.0 |
added 47 characters in body
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| Aug 8, 2016 at 19:31 | comment | added | Sasha | I don't quite see why do you think a conic bundle constructed from a conic $Q$ satisfies $C(k) \ne 0$. In fact, $Q$ is not a fiber of this conic bundle. On a contrary, fibers are conics residual to Q. | |
| Aug 8, 2016 at 17:05 | history | asked | Daniel Loughran | CC BY-SA 3.0 |