Timeline for Fiber product of singular varieties
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 19, 2019 at 4:37 | comment | added | Winnie_XP | @abx Dear abx: Thanks for your reply! that's exactly what I was expecting for, that the fiber product should have an embedded component along Z. (I did the cuspidal curve case, but I struggled in my example since I had trouble finding the kernel for the tensor product of $\mathbb{C}$ algebras. I might will try to hit Macaulay 2, lol.) | |
| Sep 19, 2019 at 4:07 | comment | added | abx | You will get the diagonal with an embedded component along $Z$; the precise structure depends very much on the particular morphism you choose. You might try first the case where $f$ is the normalization of the cuspidal cubic $y^2=x^3$ to see what happens. Your example is doable in the same way, though more complicated. | |
| Sep 19, 2019 at 1:45 | history | edited | Winnie_XP | CC BY-SA 4.0 |
added 1 character in body
|
| Sep 19, 2019 at 1:35 | history | edited | Winnie_XP | CC BY-SA 4.0 |
added 1057 characters in body
|
| Sep 19, 2019 at 1:28 | history | edited | Winnie_XP | CC BY-SA 4.0 |
added 1057 characters in body
|
| Sep 19, 2019 at 1:15 | comment | added | Winnie_XP | Thanks for the comment. Probably I should be more precise, what I would like to ask is, what is the scheme structure of $X\times_Y X$? For example, the base set is just the diagonal $\Delta_X$ union with the double point set, but as a scheme there should be a non-reduced structure along the non-immersion locus, I suppose. My question was to ask this scheme structure. | |
| Sep 18, 2019 at 20:15 | review | Close votes | |||
| Sep 23, 2019 at 3:05 | |||||
| Sep 18, 2019 at 9:23 | comment | added | abx | The first one is $X$, and the second one $X\times_YX$. This has nothing to do with singularities, or with the special properties of $f$ — just compose the appropriate cartesian diagrams. The question would be a better fit for MSE. | |
| Sep 18, 2019 at 9:10 | history | edited | YCor | CC BY-SA 4.0 |
fixed typos
|
| Sep 18, 2019 at 8:51 | history | asked | Winnie_XP | CC BY-SA 4.0 |