Timeline for How to find the action of an automorphism on the 27 lines on a cubic surface?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 14, 2012 at 16:26 | vote | accept | TonyS | ||
| Sep 13, 2012 at 17:27 | history | edited | TonyS | CC BY-SA 3.0 |
added 587 characters in body
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| Sep 12, 2012 at 16:19 | answer | added | Jérémy Blanc | timeline score: 5 | |
| Sep 12, 2012 at 12:18 | comment | added | rita | @Sasha: if you blow up a point and then a point on the corresponding exceptional curve you end up with a -2 curve. So the cubic surface won't be smooth. | |
| Sep 12, 2012 at 9:26 | comment | added | Sasha | Note that for generic blowup of 6 points on $P^2$ there are no triple intersections of lines, so this is a blowup of a very special configuration. I would guess that you should take a cubic curve on $P^2$, choose 3 inflection points, blow them up, and then blowup thee points of the intersection of the exceptional divisors with the proper preimage of the cubic curve. | |
| Sep 12, 2012 at 8:35 | comment | added | rita | I don't know if this remark is of any help, but the triple of lines $E_1$, $\sigma(E_1)$, $\sigma^2(E_1)$ is characterized by the fact that the three lines go through one point (the preimage of the flex). Also, the lines $E_1, \dots E_6$ project to 6 distinct inflection lines $l_1,\dots l_6$. A first step would be to understand whether any subset of the 9 inflection lines can occur as $l_1,\dots l_6$ | |
| Sep 11, 2012 at 18:34 | history | asked | TonyS | CC BY-SA 3.0 |