Timeline for Building a hypersurface from hyperplane sections
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 4, 2020 at 21:17 | comment | added | Sasha | @Mark: Consider the simplest example: $n = 2$, $d = 1$. You have a triangle of lines on $\mathbb{P}^2$. Imagine you have a point on each of the lines, away from their intersection points. This configuration of $V_i$ automatically satisfies your compatibility condition in the projectivized spaces of sections. But of course, not every such triple is collinear. | |
| Jan 4, 2020 at 14:23 | comment | added | Mark | Thanks! This is a big help, but I'm still missing something. I really get the $V_i$ as elements of $\mathbb PH^0(P_i,\mathcal O(d))$, so I still need to be able to check whether they have lifts to $H^0(P_i,\mathcal O(d))$ that agree in the sense you describe. Is there any easy way to see this? | |
| Jan 4, 2020 at 7:12 | history | answered | Sasha | CC BY-SA 4.0 |