Timeline for Leray-Hirsch theorem for Dolbeault cohomology
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 6, 2020 at 6:36 | vote | accept | Max Reinhold Jahnke | ||
| Mar 6, 2020 at 6:36 | answer | added | Max Reinhold Jahnke | timeline score: 1 | |
| S Dec 25, 2019 at 3:02 | history | bounty ended | CommunityBot | ||
| S Dec 25, 2019 at 3:02 | history | notice removed | CommunityBot | ||
| S Dec 17, 2019 at 1:49 | history | bounty started | Max Reinhold Jahnke | ||
| S Dec 17, 2019 at 1:49 | history | notice added | Max Reinhold Jahnke | Draw attention | |
| S Oct 2, 2017 at 21:24 | history | bounty ended | CommunityBot | ||
| S Oct 2, 2017 at 21:24 | history | notice removed | CommunityBot | ||
| S Sep 24, 2017 at 19:33 | history | bounty started | Max Reinhold Jahnke | ||
| S Sep 24, 2017 at 19:33 | history | notice added | Max Reinhold Jahnke | Authoritative reference needed | |
| Sep 14, 2017 at 3:34 | comment | added | user40276 | The degeneration (in some specific cases) which I was talking about is a theorem by Deligne which implies, for instance, the degeneration for proper submersions of Kähler manifolds that restrict on each fiber to a Kähler manifold. The original reference is numdam.org/article/PMIHES_1968__35__107_0.pdf. With a fast search on google, I've found this exposition too math.harvard.edu/~yifei/Deligne_paper.pdf (I don't know if it's good, I haven't read it carefullly). Maybe I can give you a more precise answer if you let me know the case that you're working with. | |
| Sep 12, 2017 at 17:30 | comment | added | Max Reinhold Jahnke | @user40276 Do you have a reference for this result? I believe that in the case I am working with I have that $R^q f_* \mathcal F$ is constant and finite dimensional. | |
| Sep 12, 2017 at 15:59 | comment | added | user40276 | For proper smooth morphisms of complex varieties there are some technical conditions that guarantee the degeneration. In any case, you will not, in general, get that tensor product unless the $R^q f_{*} \mathscr{F}$ is constant sheaf of $k$-module of finite dimension (I'm assuming that $\mathscr{F}$ is a sheaf of $k$-modules ). The point is that in general the sheaf of differential forms is not acyclic since there's no partition of unity in the algebraic and holomorphic case (that's the whole point of using hypercohomology). | |
| Sep 12, 2017 at 11:08 | history | edited | Max Reinhold Jahnke | CC BY-SA 3.0 |
I just corrected a typo.
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| Sep 8, 2017 at 13:41 | history | asked | Max Reinhold Jahnke | CC BY-SA 3.0 |