Timeline for The Serre duality theorem intuition
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 6, 2023 at 6:26 | comment | added | Pulcinella | It's not that useful for intution, but it's a cool fact that Serre duality (for line bundles on flag manifolds $G/B$) comes up in the Borel Weil Bott Theorem - the involution $L\mapsto L^{-1}\otimes \omega_{G/B}$ corresponds to the ($\rho$ shifted) Cartan involution on the weight lattice with fixed point $\omega^{-1/2}_{G/B}$ corresponding to $-\rho$. You can see this e.g. in the symmetry between $H^0(\mathbf{P}^1,\mathcal{O}(+n-1))$ and $H^1(\mathbf{P}^1,\mathcal{O}(-n+1))$ for $n\ge 0$. | |
| Apr 23, 2020 at 13:58 | vote | accept | user267839 | ||
| Apr 22, 2020 at 8:32 | answer | added | Leo Alonso | timeline score: 15 | |
| Apr 22, 2020 at 0:00 | history | edited | YCor | CC BY-SA 4.0 |
fixed typo
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| Apr 21, 2020 at 23:53 | history | asked | user267839 | CC BY-SA 4.0 |