Timeline for A question on curves on a hypersurface
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 20, 2022 at 10:35 | answer | added | Jason Starr | timeline score: 1 | |
| Jul 20, 2022 at 10:04 | comment | added | Jason Starr | I said something wrong in my previous comment. There is a quadratic bound for all reduced curves. | |
| Jul 20, 2022 at 7:24 | comment | added | Kim | @JasonStarr Thanks! Does this example exist on quintic 3fold? The main example I am considering is quintic 3fold, and I find such inequality for all closed subschemes of dim 1(possibly non-reduced) will be really useful. But I did not find this in books or papers. Maybe it is well-known that one can get a bound of $g$ by $F(d)$ for all one-dimensional closed subschemes, using the results for integral curves? | |
| Jul 19, 2022 at 17:22 | comment | added | Jason Starr | I do not quite understand this question. For $n\geq 4$, it is quite possible for such a hypersurface to contain, for every integer $g\gg 0$, a degree-$2$, nonreduced curve $Z$ whose reduced scheme is a line and whose nilradical is an invertible sheaf on that line of degree $-g-1$. Do you want to assume that $Z$ is reduced? | |
| Jul 18, 2022 at 18:31 | history | edited | Kim |
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| Jul 18, 2022 at 18:19 | history | asked | Kim | CC BY-SA 4.0 |