Timeline for When is Bialynicki-Birula decomposition a paving?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 3, 2021 at 20:48 | comment | added | Anton Mellit | Your claim is false, see "Białynicki-Birula, Some properties of the decompositions of algebraic varieties determined by actions of a torus. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), no. 9, 667–674", example 1. This is a blow up of $P^2$ with action with weights $(1,2,3)$ in the hyperbolic fixed point. The closure of a cell doesn't have to be a union of other cells. Your answer and its apparent popularity kind of confirms my complaint about the issue being ignored. | |
| Nov 3, 2021 at 8:51 | comment | added | Anton Mellit | I see. I edited your answer to include "some". So everything would follow from this statement that it is the union of some $W_j$. Can you prove this statement? | |
| Nov 3, 2021 at 8:47 | history | edited | Anton Mellit | CC BY-SA 4.0 |
Added the word "some"
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| Nov 3, 2021 at 4:45 | comment | added | Sasha | @AntonMellit: I do not mean it is the union of all $W_j$ with $j < i$; I mean it is the union of some $W_j$ with $j < i$. | |
| Nov 2, 2021 at 18:06 | comment | added | Sasha | @AntonMellit: where did I write $W_i \subset \overline{W_{i+1}}$? | |
| Nov 2, 2021 at 12:46 | history | answered | Sasha | CC BY-SA 4.0 |