Timeline for Maximum number of nodes in a complete intersection of two smooth hypersurfaces
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 2, 2019 at 12:45 | comment | added | user130022 | Thank you very much. I will do that. | |
| Apr 2, 2019 at 12:40 | comment | added | Jason Starr | @user130022. If you would like to ask another question, then I suggest that you post it as a separate question. I also recommend that you spend time thinking about just what you precisely want to ask. | |
| Apr 2, 2019 at 12:34 | comment | added | user130022 | Yes. I am sorry for that. But what could be the right number if one of the intersecting hypersurfaces is sufficiently general ? | |
| Apr 2, 2019 at 12:31 | comment | added | Jason Starr | @user130022. You did not ask what is the number of nodes if the hypersurfaces are "sufficiently general". You asked, and I quote: "Let $Y$ be a intersection of two smooth hypersurfaces of degree $m$ and $n$ in $\mathbb{P}^3$, where $m,n \geq 5$. Then my question is how many node $Y$ can have ?" | |
| Apr 2, 2019 at 12:23 | comment | added | user130022 | Thanks for the answer. However i think that bound can be reduced if one of the intersecting hypersurface is sufficiently general. For example if $𝑋$ is a general hypersurface of degree ≥5, then any hyperplane section can have at most $3$ nodes. projecteuclid.org/download/pdf_1/euclid.jdg/1214454680 Proposition 3. In the above example i think neither $F$ nor $G$ is sufficiently general. | |
| S Apr 2, 2019 at 11:51 | history | answered | Jason Starr | CC BY-SA 4.0 | |
| S Apr 2, 2019 at 11:51 | history | made wiki | Post Made Community Wiki by Jason Starr |