Timeline for When is Bialynicki-Birula decomposition a paving?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 10, 2021 at 21:40 | comment | added | Gjergji Zaimi | There is an article "Filtrations of meromorphic $\mathbb{C}^*$-actions on complex manifolds" by Carrell and Sommese that is essentially about this question, but I am not sure if you would find their criteria useful (corollaries 1-4). | |
| Nov 3, 2021 at 0:29 | comment | added | Geordie Williamson | I'd be very interested to hear if you do find something though... | |
| Nov 3, 2021 at 0:29 | comment | added | Geordie Williamson | ahh OK. I have vague recollections of looking at the the relatively easy case of non-projective complete toric varieties (e.g. discussed in Fulton) and thinking it was a bit tricky. Other than that I have nothing to add. | |
| Nov 2, 2021 at 21:13 | comment | added | Anton Mellit | I agree that for projective varieties it is clear. I was wondering if there's some more general argument. | |
| Nov 2, 2021 at 19:23 | comment | added | Geordie Williamson | To get a paving, it is enough to assume that X admits a $\mathbb{C}^*$-equivariant embedding inside some projective space $\mathbb{P}(V)$ with linear $\mathbb{C}^*$-action. In my experience this is often enough to get what you want. If you want to be more fancy: it is enough for $X$ to admit an ample and $\mathbb{C}^*$-equivariant line bundle. | |
| Nov 2, 2021 at 18:19 | history | became hot network question | |||
| Nov 2, 2021 at 12:46 | answer | added | Sasha | timeline score: 4 | |
| Nov 2, 2021 at 10:19 | history | asked | Anton Mellit | CC BY-SA 4.0 |