Timeline for Torus actions with more than one fixed point
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1, 2016 at 23:52 | vote | accept | Sergio Da Silva | ||
| Nov 22, 2016 at 11:28 | answer | added | Jason Starr | timeline score: 2 | |
| Nov 21, 2016 at 21:10 | comment | added | Jason Starr | @t3suji. You are correct. In the non-normal examples I had in mind, the torus action does not actually linearize to an ample invertible sheaf. | |
| Nov 21, 2016 at 21:07 | comment | added | t3suji | @Jason: it seems to me that if the action is linearized, normality is not required. If a torus acts linearly on the projective space, then the closure of any non-zero-dimensional orbit contains at least two fixed points (e.g., if T=Gm, they are lim(tx) when t->0 and when t->infty). This implies the statement. | |
| Nov 20, 2016 at 20:42 | comment | added | Jason Starr | This can fail for a non-normal variety. For a normal variety, a general orbit closure will also be normal, hence a toric variety. For a toric variety, every maximal cone comes with a torus-invariant point. If the toric variety is projective, it contains at least two maximal cones (and the projective line has precisely two maximal cones). | |
| Nov 20, 2016 at 20:30 | comment | added | T. Amdeberhan | See if this helps: chromotopy.org/torus-actions-maximal-tori-1 | |
| Nov 20, 2016 at 20:26 | history | asked | Sergio Da Silva | CC BY-SA 3.0 |