Timeline for Is there an quasi-elliptic fibration on a singular normal quartic surface?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 6, 2016 at 17:50 | comment | added | Jason Starr | Perhaps I also miswrote. | |
| Aug 6, 2016 at 14:11 | comment | added | Sándor Kovács | Jason, of course you are right. I got stuck thinking in char 0 even though the OP clearly said otherwise... At the same time you probably didn't write exactly what you meant.... :) | |
| Aug 6, 2016 at 12:33 | comment | added | Jason Starr | @SándorKovács. "If the general fiber is singular, then $X$ is not normal." That is not correct. If the function field of the base $\mathbb{P}^1$ is $k(t)$, and if the generic fiber is affine locally the zero scheme in $\mathbb{A}^2_{k(t)}$ of the polynomial $y^2-x^3-t$, then the fiber is normal, and even regular, even though it is not smooth over $k(t)$. | |
| Aug 5, 2016 at 13:59 | comment | added | Dimitri Koshelev | I am interested in the case when X has one elliptic singularity. | |
| Aug 5, 2016 at 13:53 | comment | added | Dimitri Koshelev | I mean by "quasi-elliptic fibration" a non-constant morphism to $\mathbb{P}^1$ such that the generic fiber is a singular irreducible curve of arithmetic genus 1. | |
| Aug 5, 2016 at 13:41 | comment | added | Jason Starr | What do you mean by "quasi-elliptic fibration"? A cone over a plane quartic curve is singular and normal, yet it admits no non-constant morphism to $\mathbb{P}^1$ with connected fibers. | |
| Aug 5, 2016 at 13:33 | history | asked | Dimitri Koshelev | CC BY-SA 3.0 |