Timeline for Natural vector bundle on flag variety coming from the variety of nilpotent matrices of fixed rank?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 2, 2019 at 1:22 | vote | accept | Zhiyu | ||
| Jul 2, 2019 at 1:12 | answer | added | Will Sawin | timeline score: 2 | |
| Jul 2, 2019 at 0:51 | history | edited | Zhiyu | CC BY-SA 4.0 |
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| Jul 2, 2019 at 0:46 | history | edited | Zhiyu | CC BY-SA 4.0 |
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| Jul 2, 2019 at 0:44 | comment | added | Zhiyu | @abx Thank you. For $k=1$, there is a natural action of $\mathbb G_m$, and it's a $\mathbb G_m$-torsor. I think what you said is correct. | |
| Jul 1, 2019 at 17:13 | comment | added | abx | It is not a $GL_k$-torsor — what would be the action?? On your flag variety there are two natural rank $k$ vector bundles $E$ (corresponding to the rank $k$ subspace of $V$) and $F$ (quotient of $V$ by the rank $n-k$ subspace); you are looking at the space $\underline{Isom}(E,F)$. It is a torsor both under $\underline{Aut}(E)$ and $\underline{Aut}(F)$. | |
| Jul 1, 2019 at 14:48 | history | asked | Zhiyu | CC BY-SA 4.0 |