Timeline for Does normalization of projective varieties preserve very ampleness
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 24, 2014 at 12:04 | vote | accept | user46578 | ||
| Apr 20, 2014 at 12:46 | comment | added | meh | Mine too :) . I think abx took the time to think out the question more thoroughly. | |
| Apr 19, 2014 at 14:56 | comment | added | Donu Arapura | OK, yes, my 2nd sentence was not carefully formulated. I was thinking of a scenario along the lines of abx 2). | |
| Apr 19, 2014 at 14:37 | comment | added | Allen Knutson | I don't understand the two comments above. Take $\mathcal O(1)$ on $\mathbb P^2$ and restrict to a nodal cubic $X$. Then $f^* L$ is degree $3$ on $\tilde X$, hence very ample, no? | |
| Apr 19, 2014 at 13:25 | answer | added | abx | timeline score: 6 | |
| Apr 19, 2014 at 12:56 | comment | added | meh | Never, sort of definitionally, unless $X$ is normal . It does stay ample. | |
| Apr 19, 2014 at 12:55 | comment | added | Donu Arapura | Not in general, because the sections of $f^*L$ need not separate points. E.g. take a nodal curve in the plane, and then normalize. | |
| Apr 19, 2014 at 12:47 | history | asked | user46578 | CC BY-SA 3.0 |