Timeline for Sections of $\mathcal{L}_{\lambda}$ on intersections of open cover on a flag variety
Current License: CC BY-SA 4.0
5 events
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| Jan 9, 2022 at 20:21 | history | edited | freeRmodule | CC BY-SA 4.0 |
added 141 characters in body; edited title
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| Jan 9, 2022 at 20:18 | comment | added | freeRmodule | @Callum ah yes sorry that is what I meant--- for each T-fixed point take a Borel subgroup containing T which has an open orbit at that point, and take this as your cover. I will update my question and have a look at your reference. Thanks! | |
| Jan 4, 2022 at 15:13 | comment | added | Callum | Perhaps you mean the open affine subsets formed by taking the "big" cell for each of a series of Borel subgroups. You can indeed form an open cover this way (and finite as well since $G/P$ is compact). I don't know the general theory of their intersections but the intersection of two complementary ones is a Richardson variety (see mathoverflow.net/questions/193867/…) | |
| Jan 3, 2022 at 2:38 | comment | added | Callum | Maybe I'm misunderstanding, but the $B$-orbits don't intersect. Orbits of a fixed group are disjoint almost by definition. $G/P$ doesn't have an open cover by these orbits, it is precisely the disjoint union of the orbits. | |
| Dec 29, 2021 at 17:16 | history | asked | freeRmodule | CC BY-SA 4.0 |