Timeline for Degree of canonical bundle?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 16, 2010 at 17:06 | answer | added | roy smith | timeline score: 1 | |
| Sep 6, 2010 at 17:25 | vote | accept | doktorkrampus | ||
| Sep 6, 2010 at 13:12 | answer | added | Angelo | timeline score: 13 | |
| Sep 6, 2010 at 13:05 | comment | added | Remke Kloosterman | In general $omega_X$ is not the restriction of a line bundle on $\mathbb{P}^n$. An example is the twisted cubic curve in $\mathbb{P}^3$. In this case the canonical bundle has degree -2, whereas every line bundle obtained by restriction has degree divisible by 3. You can have a look on the final section of chapter IV of Hartshorne. He gives a discussion which pairs (d(C),g(C)) are possible for smooth space curves C. In particular, it is shown that for fixed d there are many possibilities for the genus of C. (Provided that d is not 1 or 2.) | |
| Sep 6, 2010 at 13:01 | answer | added | Daniel Loughran | timeline score: 5 | |
| Sep 6, 2010 at 12:51 | comment | added | Daniel Loughran | Complete interesections are quite special among projective varieties. I am doubtful as to whether there is much to say for an arbitrary projective variety. | |
| Sep 6, 2010 at 12:27 | history | asked | doktorkrampus | CC BY-SA 2.5 |