Timeline for Resolution of the pushforward of a vector bundle
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 30, 2022 at 11:27 | comment | added | Will Sawin | Probably there is no way to do it by modifying the Koszul complex and you need to use a different method (e.g. twisting by ample line bundles and taking global sections) | |
| May 30, 2022 at 11:04 | comment | added | BinAcker | @WillSawin I indeed did not assume that $F$ comes from a restriction of a bundle on $X$ | |
| May 30, 2022 at 10:30 | comment | added | Will Sawin | If $F$ extends to a holomorphic vector bundle $G$ on $X$, then you want to tensor each term with $G$ to obtain a resolution of $i_* F=( i_* \mathcal O(Z)) \otimes G$. If not, then I don't think Z. M's idea will help. | |
| May 30, 2022 at 8:47 | comment | added | BinAcker | @Z.M I guess that in your analogy $\mathcal{F}$ is $\mathcal{O}(Z)$ for me, but what would be $\mathcal{E}$ ? I would be grateful if you could develop a little | |
| May 30, 2022 at 7:59 | comment | added | Z. M | Apply the projection formula. | |
| May 30, 2022 at 7:56 | history | asked | BinAcker | CC BY-SA 4.0 |