Timeline for Structure of iterated $\mathbb{P}^1$-bundles
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Oct 23, 2010 at 13:33 | comment | added | Piotr Achinger | But the point is that e.g. the Bott-Samelson varieties are not toric in general, and I would like to include them as well. Probably I should consider such towers with a $B$-action instead of $T$-action (the toric ones would then have this $B$-action factored through the projection $B\to T$). | |
| Oct 23, 2010 at 3:12 | comment | added | Sasha | Certainly, if you restrict to the toric case, a combinatorial description is possible and I guess is quite simple. | |
| Oct 22, 2010 at 21:56 | comment | added | Piotr Achinger | Dear Sasha, that's a good point! But maybe, as in the framework of toric varieties, we can restrict ourselves to some "uniform" or "equivariant" rank two bundles, in which case there would be some good description (a class wide enough to include examples that appear in nature)? Note that every uniform rank two vector bundle on the quadric splits and that equivariant bundles on toric varieties have a good description. | |
| Oct 22, 2010 at 18:53 | comment | added | Sasha | You cannot hope to have a simple combinatorial description --- the theory of rank 2 vector bundles on $P^1\times P^1$ is already rather complicated. | |
| Oct 22, 2010 at 15:21 | answer | added | Dave Anderson | timeline score: 2 | |
| Oct 22, 2010 at 15:20 | comment | added | Dave Anderson | Hi Piotr -- you might add "effectiveness" of line bundles to your first item... though I expect such a thing might be complicated in general. | |
| Oct 22, 2010 at 14:28 | history | asked | Piotr Achinger | CC BY-SA 2.5 |