Timeline for $\mathbb{C}^{*}$-actions on Fano $3$-folds
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 23, 2018 at 8:01 | vote | accept | Nick L | ||
| Jul 23, 2018 at 6:37 | comment | added | Jérémy Blanc | @NickL You are absolutely right. Sorry for this. I removed my comment. | |
| Jul 23, 2018 at 6:10 | comment | added | Nick L | I don't understand the first part of your comment, since condition 1) is that there is finite fixed points, so to relax this condition means that we don't require there to be finite fixed points; all I am saying is that $\mathbb{P}^{1} \times S$ satisfies 2. and 3 but not 1. | |
| Jul 22, 2018 at 22:18 | answer | added | Jérémy Blanc | timeline score: 3 | |
| Jul 17, 2018 at 21:38 | history | edited | Nick L | CC BY-SA 4.0 |
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| Jul 17, 2018 at 21:12 | history | edited | Nick L | CC BY-SA 4.0 |
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| Jul 17, 2018 at 21:11 | comment | added | Nick L | I meant that the fixed point set it isolated. But thanks for the example! I did not know that one. | |
| Jul 17, 2018 at 19:30 | comment | added | Jonny Evans | Do you mean all fixed points are isolated, or that there exist isolated fixed points? If the latter, you could take the blow up of P^3 along a twisted cubic: this has a Moebius group action, since P^3=Sym^3(P^1), and the twisted cubic is an orbit (triples of coincident points). A C^* inside the Moebius group has four isolated fixed points, two on the twisted cubic, so I guess these become fixed P^1s after blowing up, but the other two fixed points are still isolated. | |
| Jul 17, 2018 at 18:40 | history | edited | Nick L | CC BY-SA 4.0 |
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| Jul 17, 2018 at 18:33 | history | asked | Nick L | CC BY-SA 4.0 |