Timeline for Embedding varieties as divisors
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 2, 2021 at 21:42 | comment | added | Evgeny Shinder | @user2831784: from the exact sequence of Picard groups for $C \setminus p \subset C$ one gets that if $K_{C \setminus p}$ is trivial, then $K = (2g-2)[p]$. This can not hold for general $p$, as if it does for points $p$ and $q$, then $[p] - [q]$ is $(2g-2)$-torsion in the Jacobian. | |
| Feb 2, 2021 at 21:16 | comment | added | user2831784 | @abx Could you explain why the canonical bundle being nontrivial on $C$ globally implies that it is nontrivial on $C \smallsetminus p$ for a general $p$? | |
| Feb 2, 2021 at 20:11 | vote | accept | GiveMeDivisorsPlease | ||
| Feb 2, 2021 at 20:11 | comment | added | GiveMeDivisorsPlease | @abx Of course, thanks!! | |
| Feb 2, 2021 at 19:29 | comment | added | abx | A smooth curve embedded into $\mathbb{A}^2$ has trivial canonical bundle. Take any smooth projective curve $C$ of genus $\geq 2$ and general point $p\in C$, then $C\smallsetminus p$ is affine with non-trivial canonical bundle. | |
| Feb 2, 2021 at 19:21 | comment | added | GiveMeDivisorsPlease | Oh wow, I feel stupid. Could you just give me an example of such a curve? Thanks so mcuh. | |
| Feb 2, 2021 at 18:56 | review | Low quality posts | |||
| Feb 2, 2021 at 20:17 | |||||
| Feb 2, 2021 at 18:49 | review | First posts | |||
| Feb 2, 2021 at 20:09 | |||||
| Feb 2, 2021 at 18:39 | history | answered | jori | CC BY-SA 4.0 |