Timeline for Borel spectral sequence with non-compact fibers
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 5, 2022 at 19:07 | history | bounty ended | CommunityBot | ||
| Feb 4, 2022 at 17:10 | vote | accept | Grisha Taroyan | ||
| Feb 2, 2022 at 11:02 | comment | added | Johannes Huisman | The complex vector space $\Omega^{p+q-s}(\mathbf C)$ of global holomorphic $(p+q-s)$-forms is the Dolbeault cohomology group $\mathrm H^{p+q-s,0}(\mathbf C)$. The higher $\mathrm H^{p+q-s,i}(\mathbf C)$, $i>0$, vanish since $\mathbf C$ is Stein. Hence, what I wrote down is the $E_2$ page allright. | |
| Feb 2, 2022 at 8:27 | comment | added | Grisha Taroyan | Somehow I thought that the second page is the tensor product of sums of homology groups, not homology and forms. Why is it the same thing? The original result of Borel says something along the lines $E_2^{p,q}=\bigoplus_{p,q} \mathrm H^{s-q,q}(B,\mathbf{H}^{p+q-s}(F)),$ where $\mathbf{H}^{p+q-s}(F)$ is the bundle of Dolbeault cohomology groups of the fibers. The term $E_1,$ however, should look like what you have written down. Maybe the passage to $E_2$ is trickier and we don't get the tensor product like in the case of Kahler fibers | |
| Feb 1, 2022 at 15:41 | history | answered | Johannes Huisman | CC BY-SA 4.0 |