Timeline for The algebra of regular functions of a quasi-affine toric variety
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 28, 2017 at 17:51 | vote | accept | Anonymous | ||
| Apr 28, 2017 at 17:51 | vote | accept | Anonymous | ||
| Apr 28, 2017 at 17:51 | |||||
| Apr 28, 2017 at 17:43 | vote | accept | Anonymous | ||
| Apr 28, 2017 at 17:51 | |||||
| Apr 28, 2017 at 15:58 | answer | added | Friedrich Knop | timeline score: 4 | |
| Apr 28, 2017 at 15:21 | answer | added | Jason Starr | timeline score: 2 | |
| Apr 28, 2017 at 15:19 | comment | added | Jason Starr | @PiotrAchinger. You beat me to it. I will post my answer anyway in a moment. | |
| Apr 28, 2017 at 15:18 | comment | added | Piotr Achinger | If $X$ is affine, corresponding to a rational cone $\sigma$ in $N_{\mathbf{R}}$, then $\Gamma(X, \mathcal{O}_X)$ is the semigroup algebra of the monoid $P_\sigma = \sigma^\vee\cap M$ ($M=N^\vee$) which is of course finitely generated. It is a subalgebra of the group algebra of $M$, which is the character group of the torus. A general toric $X$ corresponds to a fan $\Sigma$ which is a collection of such cones $\sigma$, and $\Gamma(X, \mathcal{O}_X)$ is the semigroup algebra of the intersection of all $P_\sigma$, $\sigma\in\Sigma$ inside $M$, which is finitely generated for the same reasons. | |
| Apr 28, 2017 at 14:23 | history | asked | Anonymous | CC BY-SA 3.0 |