Timeline for Exterior product of Euler Exact Sequence
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 10, 2023 at 3:49 | comment | added | R. van Dobben de Bruyn | Ah right, in this case $\bigwedge^i \mathcal O_{\mathbf P^n} = 0$ for $i \geq 2$, so you just get a bunch of short exact sequences $0 \to \bigwedge^{i-1}\mathcal T_{\mathbf P^n} \to \bigwedge^i \mathcal O_{\mathbf P^n}(1)^{n+1} \to \bigwedge^i \mathcal T_{\mathbf P^n} \to 0$. | |
| Feb 10, 2023 at 2:26 | comment | added | BVquantization | thanks, if I well understood, we have $ \bigwedge^2\mathcal{T}_{\mathbb{P}^n} \cong \frac{\bigwedge^2\mathcal{O}(1)^{n+1}}{\mathcal {T}_{\mathbb {P}^n} } $ | |
| Feb 10, 2023 at 0:51 | comment | added | R. van Dobben de Bruyn | See for instance Hartshorne, Exercise II.5.16 for turning short exact sequences of vector bundles into filtrations computing their symmetric or exterior powers. | |
| Feb 10, 2023 at 0:49 | history | asked | BVquantization | CC BY-SA 4.0 |