Timeline for Union of Schubert cells being affine
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 27, 2020 at 14:15 | answer | added | Igor Makhlin | timeline score: 3 | |
| May 26, 2020 at 13:02 | comment | added | Igor Makhlin | @Sasha, thanks. By "disjoint" do you mean that each cell in $Z$ has a neighborhood in $\mathcal F$ that is pointwise disjoint from every other cell in $Z$ (equivalently: the topology on $Z$ induced from $\mathcal F$ is the disjoint union topology)? This property obviously holds if and only if the $w\in S$ are pairwise Bruhat-incomparable. What stops your argument from working in this more general case? | |
| May 26, 2020 at 4:53 | comment | added | Sasha | @imakhlin: The union of cells of equal dimension is a disjoint union of affine varieties, hence affine. | |
| May 26, 2020 at 1:37 | comment | added | Igor Makhlin | Do you have a reference for the union of cells of equal dimension being affine? (Or is it obvious and I'm just not seeing it?) | |
| May 25, 2020 at 15:30 | history | edited | KKD | CC BY-SA 4.0 |
added 20 characters in body
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| May 25, 2020 at 14:50 | comment | added | LSpice | Sorry, yes. I missed that CJS was taking the union of the cells in $\mathcal F$, not in $G$. | |
| May 25, 2020 at 14:50 | comment | added | Sam Hopkins | @LSpice: huh? Wouldn't $S=W$ give the whole flag variety? | |
| May 25, 2020 at 14:48 | comment | added | LSpice | It's certainly not the only case; you can take $S = W$, for example. | |
| May 25, 2020 at 14:48 | history | edited | LSpice | CC BY-SA 4.0 |
TeX fix
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| May 25, 2020 at 13:44 | history | asked | KKD | CC BY-SA 4.0 |