Timeline for When simple cohomological computations predict ingenious algebro-geometric constructions?
Current License: CC BY-SA 4.0
Post Revisions
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 11, 2021 at 19:23 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Aug 30, 2019 at 21:15 | answer | added | Squid with Black Bean Sauce | timeline score: 6 | |
| Aug 18, 2019 at 12:26 | history | edited | Turbo |
edited tags
|
|
| Aug 17, 2019 at 22:27 | comment | added | Daniil Rudenko | @Libli I guess, agree with you in historical perspective. On the other hand, now for many people cohomology, MHS and motives are far more familiar objects than «quadratic line complexes», polar correspondence etc. The goal of this question is to collect a few examples of that. | |
| Aug 17, 2019 at 21:15 | comment | added | Daniil Rudenko | Thanks for the references! I guess that indeed there are countless known examples, so my idea behind this question was to get a list of "favorite" examples. | |
| Aug 16, 2019 at 2:25 | comment | added | Timothy Chow | Although it doesn't involve Hodge structures, maybe the following sort of situation interests you? There is a simply defined, natural group action on cohomology, and one suspects that it arises from a group action on the variety, but the latter is unknown. If so, then a concrete example is Tymoczko's "dot action" on the cohomology of certain subvarieties of the flag variety (Hessenberg varieties), which in general is not known to come from a group action on the varieties themselves. See arxiv.org/abs/0706.0460 especially Section 5.2. | |
| Aug 15, 2019 at 14:37 | comment | added | Libli | As far as "Mathematics" (with a big M) is concerned, I believe things go the other way round. People usually first notice a more or less simple phenomenon occuring in some examples (geometric for instance). Then, they try to simplify and generalize it using more abstract mathematical structures (say Hodge structures for instance). This is at least the way Grothendieck thought about Algebraic Geometry. | |
| Aug 15, 2019 at 13:26 | comment | added | dhy | There are many examples involving cubic fourfolds - see arxiv.org/abs/1601.05501. | |
| Aug 15, 2019 at 11:39 | comment | added | LSpice | I don't know about the durability of Semantic Scholar links, but this paper is also on Reid's home page: Reid - The complete intersection of two or more quadrics. | |
| Aug 15, 2019 at 11:38 | history | edited | LSpice | CC BY-SA 4.0 |
Name of paper
|
| Aug 14, 2019 at 21:04 | history | asked | Daniil Rudenko | CC BY-SA 4.0 |