Timeline for Zero loci of sections of wedge product of bundles
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 29, 2023 at 12:42 | vote | accept | Kim | ||
| Nov 29, 2023 at 7:28 | answer | added | Sasha | timeline score: 1 | |
| Nov 29, 2023 at 1:20 | comment | added | Kim | @Sasha Now I see what you mean. Could you briefly explain what happens for $\mathrm{rank}(\xi)=4$, or point out any reference? | |
| Nov 28, 2023 at 17:49 | comment | added | Sasha | No. I just want to say that in the case where $\dim V = 5$ there are two isomorphism classes of zero loci --- one (that corresponds to $\xi$ with $\mathrm{rank}(\xi) = 2$) can be indeed written as $G \cap \mathbb{P}(W_2 \wedge V)$ (where $W_2$ is the 2-dimensional subspace that orresponds to $\xi$) but the other (that corresponds to $\xi$ with $\mathrm{rank}(\xi) = 4$) is quite different. | |
| Nov 28, 2023 at 13:39 | comment | added | Kim | @Sasha Thanks! So you mean the above description holds when $rk(\xi)\neq 2$ and $4$? How about $rk(\xi)= 2$ or $4$ cases? It seems like the zero locus is determined by $ker(\xi)$. | |
| Nov 28, 2023 at 7:46 | comment | added | Sasha | A global section of $\wedge^2F$ is a bivector $\xi \in \wedge^2V$. The description of its zero locus is different in the case where the rank of $\xi$ is 4 or 2. | |
| Nov 28, 2023 at 4:14 | history | edited | Kim | CC BY-SA 4.0 |
added 58 characters in body
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| Nov 28, 2023 at 3:56 | history | asked | Kim | CC BY-SA 4.0 |