Timeline for Different occurences of the word 'period' in algebraic geometry
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 28, 2021 at 9:08 | comment | added | Cranium Clamp | @Z.M I found most of the details of that relative second cohomology group and the integral (which is $ \zeta(2) $) in the paper of Francis Brown here: arxiv.org/abs/math/0606419 | |
| Dec 27, 2021 at 16:39 | comment | added | Z. M | Periods are more general than that (I am not sure whether this kind of "periods" also dates back to the 19th century). Kontsevich–Zagier gave several examples like $\log(2)$ and $\zeta(3)$ right after the first definition. The MO question that OP linked also contains an example $\int_{0\le x\le y\le1}(1-x)^{-1}y^{-1}\mathrm{d}x\mathrm{d}y$, but I don't understand their $H^2(\overline{M_{0,5}}\setminus A,B\setminus(A\cap B))$. | |
| Dec 27, 2021 at 16:05 | comment | added | Misha Verbitsky | If I understand correctly, you should take the Riemann surface of this function in the complex 2-space with coordinates (x, y), and integrate the form dx/y along the path which lifts this interval to one branch until the branching point, then goes around this point and goes back along another lift of this interval, but on a different branch. | |
| Dec 27, 2021 at 15:58 | comment | added | Misha Verbitsky | There is a detailed argument in this paper arxiv.org/pdf/1504.04405.pdf The Origins of Complex Geometry in the 19th Century (Raymond O. Wells, Jr.), Section 6 | |
| Dec 24, 2021 at 23:14 | comment | added | Z. M | Sorry for a silly question: how to rewrite $\int_0^r\mathrm{d}x/\sqrt{4x^3-ax-b}$ (in the second of the original post) as an integral over a closed cycle on a Riemann surface? | |
| Dec 24, 2021 at 14:32 | history | edited | Misha Verbitsky | CC BY-SA 4.0 |
added 1 character in body
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| Dec 24, 2021 at 9:43 | vote | accept | Cranium Clamp | ||
| Dec 23, 2021 at 12:13 | history | answered | Misha Verbitsky | CC BY-SA 4.0 |