Timeline for Is it possible to find infinitely many points in a smooth variety such that their dual of corresponding tangent space have nonzero intersection?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 19, 2021 at 11:53 | comment | added | Zach Teitler | I was thinking of a hyperplane tangent along a line in $X$. | |
| May 19, 2021 at 6:59 | comment | added | Leo D | Thanks @abx for your beautiful example. The idea of considering the Veronese makes everything so concrete. | |
| May 19, 2021 at 6:54 | comment | added | Leo D | @ZachTeitler if I didn't meantion that X is smooth, there you are right there are a lot of counter examples---those who contain linear components. But if I require smoothness, then maybe there is only one exceptional, the hyperplane. | |
| May 19, 2021 at 6:06 | comment | added | abx | I am not sure I understand the question : as the OP mentions, there are no such examples with hypersurfaces. All you need is a hyperplane section with a singular locus of dimension $>0$ —which can of course be a linear subspace. | |
| May 19, 2021 at 5:23 | comment | added | Zach Teitler | Are there additional examples whenever the variety contains a linear subspace? Those are plentiful including for hypersurfaces. | |
| May 19, 2021 at 4:46 | history | answered | abx | CC BY-SA 4.0 |