Timeline for Conditions for a smooth scheme of finite type with trivial class group to be quasi-affine
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 30, 2016 at 7:56 | comment | added | sabrebooth | Thank you for the counter-example, this is enlightening. However, it turns out that if you also ask the scheme $X$ to be separated, then it has to be quasi-affine. Actually, any normal variety with a trivial class group is a quasi-affine variety. This can be seen for instance by using the notion of ample family of line bundles. A normal variety with trivial class group always has such an ample family which turns out to be a singleton (since the Picard group is trivial), and thus the structure sheaf itself is ample, which is equivalent to being quasi-affine. | |
| Apr 30, 2016 at 7:46 | vote | accept | sabrebooth | ||
| Apr 29, 2016 at 16:28 | history | edited | Takumi Murayama | CC BY-SA 3.0 |
Grammar
|
| Apr 29, 2016 at 15:28 | history | answered | Takumi Murayama | CC BY-SA 3.0 |