Timeline for Curvature forms of holomorphic line bundles
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 22, 2022 at 18:54 | answer | added | Misha Verbitsky | timeline score: 1 | |
| Jun 3, 2022 at 4:27 | comment | added | Richard Lärkäng | Regarding your second question, it seems like the Chern connection associated to a hermitian metric on $\mathcal{O}_{\mathbb{P}^n}(1)$ would answer that. | |
| Jun 3, 2022 at 4:22 | comment | added | Richard Lärkäng | It certainly can contain a $(2,0)$-component. In general, if $\theta$ is the connection matrix in a local frame, then the curvature is $\Theta=d\theta+\theta^2=d\theta$ (since $\theta$ is a $1$-form). Locally, the connection matrix could be any $1$-form, and if it is compatible with $\bar\partial$, it could be any $(1,0)$-form. | |
| Jun 2, 2022 at 12:20 | history | asked | Dave Shulman | CC BY-SA 4.0 |