Timeline for Understanding the maps of the long exact sequence of cohomology from a Koszul complex
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 10 at 14:35 | comment | added | Sasha | If you look at the proof of the Borel--Bott--Weil Theorem (e.g., in the paper of Demazure) you will see that $H^m$ iis identified, eventually, with $H^0$ of a different bundle, and typically $s$ induces a morphism between those. | |
| Jan 10 at 11:22 | history | edited | ett | CC BY-SA 4.0 |
added 21 characters in body
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| Jan 10 at 11:18 | comment | added | abx | Sorry, I thought you were asking about $H^0$. I don't think Bott's theorem tells you anything about $H^m$ (or $H^0$, for that matter). | |
| Jan 10 at 10:49 | comment | added | ett | We know how it acts on the global sections, but I am not sure how to translate this to higher cohomologies. I know how to understand what $H^m(\bigwedge^i\mathcal E^\ast)$ is via Bott's theorem, but I cannot see how to translate this map, that I know how it works on the global section level, to higher cohomologies. | |
| Jan 10 at 10:38 | comment | added | abx | I don't understand the question. The map $\phi_i$ is explicit (interior product with $s$), so don't we know how it acts on global sections? | |
| S Jan 10 at 10:31 | review | First questions | |||
| Jan 10 at 10:33 | |||||
| S Jan 10 at 10:31 | history | asked | ett | CC BY-SA 4.0 |