Timeline for Singular curves in a 3-fold?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 20, 2011 at 8:24 | comment | added | Qing Liu | Note that if the base field is imperfect, then even the local statement fails (but OK if replace smooth with regular). | |
| Jul 19, 2011 at 23:45 | comment | added | Qing Liu | Once you know that the tangent space of $C$ at the singular point has dimension $2$ (see Hailong Dao's answer and Jason Starr's comment), if $X$ is quasi-projective over a perfect infinite field, then $C$ is contained in a smooth hypersurface of $X$, see Kleiman-Altman: ''Bertini theorems for hypersurfaces containing a subscheme'', Proposition (6). Over a finite field, Poonen : ''Bertini theorems over finite fields'', Theorem 1.3 should do the trick. | |
| Jul 19, 2011 at 19:49 | vote | accept | mrw | ||
| Jul 19, 2011 at 14:21 | answer | added | Hailong Dao | timeline score: 4 | |
| Jul 19, 2011 at 13:46 | answer | added | Jason Starr | timeline score: 5 | |
| Jul 18, 2011 at 21:02 | history | asked | mrw | CC BY-SA 3.0 |