Timeline for Maximum number of nodes in a complete intersection of two smooth hypersurfaces
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 2, 2019 at 12:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 2, 2019 at 11:51 | answer | added | Jason Starr | timeline score: 2 | |
| Apr 2, 2019 at 10:07 | comment | added | user130022 | projecteuclid.org/download/pdf_1/euclid.jdg/1214454680 Proposition 3 in the mentioned article. | |
| Apr 2, 2019 at 10:04 | comment | added | user130022 | If $X, Y$ are general smooth hypersurface and their intersection is singular at a point, then it is clear that $X$ and $Y$ are tangential at that point. Now question is at how many points they are tangential to each other. | |
| Apr 2, 2019 at 10:03 | comment | added | Francesco Polizzi | " if $X$ is a general hypersurface of degree $≥5$, then any hyperplane section can have at most $3$ nodes". Why this? | |
| Apr 2, 2019 at 9:57 | comment | added | user130022 | Yes. That will give an bound for sure. But i want something more effective bound. For example if $X$ is a general hypersurface of degree $\ge 5$, then any hyperplane section can have at most $3$ nodes, which is much smaller than its genus. | |
| Apr 2, 2019 at 8:36 | comment | added | Francesco Polizzi | Did you try to compute the arithmetic genus of the intersection with the genus formula in order to obtain an upper bound for the number of nodes? | |
| Apr 2, 2019 at 8:20 | history | asked | user130022 | CC BY-SA 4.0 |