Timeline for Does every finite map of smooth varieties birationally embed as a smooth hypersurface of 1d trivial bundle over the base?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 21, 2023 at 16:50 | vote | accept | Kevin Casto | ||
| Mar 21, 2023 at 13:50 | answer | added | Jason Starr | timeline score: 4 | |
| Mar 20, 2023 at 12:50 | answer | added | Roberto Pignatelli | timeline score: 3 | |
| Mar 20, 2023 at 0:09 | comment | added | Kevin Casto | @JasonStarr Great! I'm happy with that case if you'd like to post an answer with a reference or explanation. | |
| Mar 19, 2023 at 23:56 | comment | added | Jason Starr | If $X$ is affine, this is true. | |
| Mar 19, 2023 at 22:41 | comment | added | Kevin Casto | For example, if $X = \mathbb A^1$ this is asking if every curve is birational to a smooth affine plane curve, which is true but takes some work. | |
| Mar 19, 2023 at 22:36 | comment | added | Kevin Casto | @JasonStarr But can $Y'$ always be chosen smooth? | |
| Mar 19, 2023 at 22:24 | comment | added | Jason Starr | That follows from the Primitive Element Theorem applied to the field extension $\mathbb{C}(X)\subset \mathbb{C}(Y)$. | |
| Mar 19, 2023 at 21:34 | history | asked | Kevin Casto | CC BY-SA 4.0 |