Timeline for Existence of a morphism between two toric varieties
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 19, 2015 at 15:28 | answer | added | Philip Engel | timeline score: 3 | |
| Sep 19, 2015 at 15:22 | comment | added | Philip Engel | Two fibers of the projection $\mathbb{P}^1\times\mathbb{P}^1\rightarrow \mathbb{P}^1$. I will make my comment an answer, to elaborate. | |
| Sep 17, 2015 at 15:22 | answer | added | Lars Kastner | timeline score: 2 | |
| Sep 17, 2015 at 12:29 | answer | added | Allen Knutson | timeline score: 3 | |
| Sep 16, 2015 at 14:02 | comment | added | Pedro Montero | In order to deal with toric varieties we should blow-up torus invariant points instead, no? If it is the case, you can consider the fan of $X=\operatorname{Bl}_{p_1,p_2,p_3,p_4}(\mathbb{P}^3)$ and project onto the $xy$-plane. This will give a toric morphism from $X$ onto the blow-up of $\mathbb{P}^1\times \mathbb{P}^1$ at two invariant points and then you can blow-down. | |
| Sep 16, 2015 at 13:53 | comment | added | user68440 | I do not understand. The fibers would be curves not sufaces. | |
| Sep 16, 2015 at 9:41 | comment | added | Jason Starr | There exists a constant morphism :) I love bad jokes. | |
| Sep 16, 2015 at 4:27 | comment | added | Philip Engel | Maybe I'm missing something, but the inverse images of two disjoint fibers are two disjoint surfaces in the blow-up. The images of these surfaces in $\mathbb{P}^3$ must then only intersect at the four points, which is impossible, as two surfaces in $\mathbb{P}^3$ always intersect in at least a curve. | |
| Sep 16, 2015 at 1:07 | history | asked | user68440 | CC BY-SA 3.0 |