Timeline for The Riemann correspondence for riemann surfaces made explicit and its generalizations
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2011 at 20:15 | answer | added | roy smith | timeline score: 6 | |
| May 18, 2010 at 13:10 | answer | added | Someone | timeline score: 0 | |
| May 18, 2010 at 8:22 | comment | added | John Stillwell | If it is correct to attribute this correspondence to Riemann (which I'm not completely sure about) then the year would be 1857, in his paper Theorie der Abel'schen Functionen, Journal für die reine und angewandte Mathematik, vol. 54 (1857), pp. 101-155. | |
| May 18, 2010 at 5:40 | answer | added | Charles Siegel | timeline score: 3 | |
| May 18, 2010 at 4:29 | comment | added | BCnrd | Corona, this is specific to dim 1 and trdeg 1. Learn alg. curves over an alg. closed field (with singularities, and without, via normalization). Then passage in reverse direction is easier to grock. Yes, Riemann et al. worked in days before algebraic geometry. But honestly, it is easier to pass from algebraic data of function field to algebro-geometric data of plane curve with singularities on to smooth possibly non-planar proj. alg. curve, which can be "analytified" than to follow the historical route and rigorously "desingularize" an "analytic singularity" by elementary analytic tools. | |
| May 18, 2010 at 3:37 | comment | added | Qiaochu Yuan | As far as the genus, see mathoverflow.net/questions/152/… . | |
| May 18, 2010 at 3:33 | comment | added | KConrad | There is no unique equation P(x,y) = 0. Simple reason: you can always replace x with x + 1. It's like in algebra, where a field extension is an intrinsic thing but it can be generated by many particular elements. | |
| May 18, 2010 at 3:17 | history | asked | Corona | CC BY-SA 2.5 |