Timeline for When is a del Pezzo surface a conic bundle?
Current License: CC BY-SA 4.0
6 events
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| Mar 25 at 11:52 | comment | added | Daniel Loughran | I'd be happy to hear more about how this question arose in your research; feel free to email me. | |
| Mar 25 at 11:52 | comment | added | Daniel Loughran | I see. This looks a bit trickier. For example take a quartic del Pezzo surface $S$ with $\mathrm{Pic} S \cong \mathbb{Z}$. Such $S$ is minimal. If $S$ admits a general rational rational point, then blowing up it yields a cubic surface with a line, hence $S$ is birational to a conic bundle surface. If $S$ admits no rational points however, then it's not clear whether it is birational to a conic bundle surface of not. | |
| Mar 25 at 11:50 | history | edited | Daniel Loughran | CC BY-SA 4.0 |
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| Mar 25 at 6:29 | comment | added | fp1 | I was originally thinking k-birational to a conic bundle. This is still a helpful answer though | |
| Mar 22 at 10:12 | history | edited | Daniel Loughran | CC BY-SA 4.0 |
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| Mar 22 at 10:06 | history | answered | Daniel Loughran | CC BY-SA 4.0 |