Timeline for Are there any special relations among the 27 lines on a cubic surface?
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| Oct 30, 2020 at 17:21 | comment | added | AUNebulosa | @Pop By complementary reguli, I mean the set of three other skew lines which also lie on the cubic surface and pairwise intersect the original three skew lines. So, if I have 6 lines, each pair of intersecting lines must yield 7 independent conditions on the cubic form, thus three pairs impose 21 conditions (at most). Shouldn't I be able to determine the cubic this way? | |
| Oct 30, 2020 at 17:13 | comment | added | AUNebulosa | @Wojowu Thank you! That's a useful link. | |
| Oct 30, 2020 at 15:38 | comment | added | Pop | I just address the question about three skew lines (and ignore the parenthetical because I don't know what "complementary reguli" means). A very simple parameter shows the answer is negative. Vanishing on a line imposes 4 conditions on a cubic form. So vanishing on 3 skew lines imposes (at most) 12 conditions. But the space of cubic forms has dimension 20. | |
| Oct 30, 2020 at 15:22 | comment | added | Wojowu | mathoverflow.net/q/257313/30186 | |
| Oct 30, 2020 at 15:18 | history | asked | AUNebulosa | CC BY-SA 4.0 |