Timeline for Is $G/T$ a projective variety?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 30, 2014 at 15:43 | vote | accept | CommunityBot | ||
| Feb 2, 2014 at 13:24 | comment | added | Lev Soukhanov | Peter's setting is a real compact group and it's complexification. If you will take complex group and it's maximal torus it won't be compact for sure. And any complex connected compact group is an abelian variety, so it's definitely not you are asking for. If you consider an algebraic setting, then $G/T$ is NEVER projective unless it's a point. But it is true that for a compact group $G$ $G/T$ is homeomorphic to the $G_\mathbf{C} / B$, which is projective and called the generalized flag variety. | |
| Feb 1, 2014 at 22:05 | comment | added | Peter Crooks | You're welcome! Compactness is definitely required for this construction to work. | |
| Feb 1, 2014 at 21:54 | comment | added | user21574 | Peter thanks for your answer, You said $G/T$ inherits the projective variety structure while Ben found an counterexample. The point is the additional conditions $G$ must be compact, connected? | |
| Feb 1, 2014 at 19:38 | history | answered | Peter Crooks | CC BY-SA 3.0 |