Timeline for Why the letter "p" for genus?
Current License: CC BY-SA 3.0
17 events
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| May 11, 2016 at 13:19 | comment | added | KConrad | @Qfwfq I have no idea. | |
| May 11, 2016 at 11:34 | comment | added | Qfwfq | @KConrad: I was convinced that the "P" in $P_g$ really came from "plurigenus". Is it so unlikely? :) | |
| Jul 7, 2015 at 2:37 | comment | added | Noam D. Elkies | Wiktionary gives several senses for род including "genus". I tried to give the link but it doesn't seem to follow; here it is in two pieces: en.wiktionary.org/wiki followed by /род | |
| Jul 12, 2012 at 19:12 | history | edited | YangMills | CC BY-SA 3.0 |
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| May 13, 2012 at 17:16 | answer | added | Abdelmalek Abdesselam | timeline score: 3 | |
| May 11, 2012 at 1:40 | answer | added | Papiro | timeline score: 1 | |
| Apr 7, 2012 at 21:49 | history | edited | YangMills |
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| Apr 5, 2012 at 13:23 | history | edited | YangMills |
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| Apr 3, 2012 at 0:08 | comment | added | KConrad | @Igor: I was just kidding in my previous comment (hence the smiley face at the end). Certainly the Russians had nothing to do with creating the notation, but I remember that when I first saw род I was struck that here was a word for genus starting with p, even though it was obviously a coincidence. Anyway, roy's comment suggests that maybe the letter p is related to the word periodische (periodic). | |
| Apr 1, 2012 at 20:50 | comment | added | roy smith | The letter p is used by Riemann in his 1857 paper on abelian functions: a surface has connectivity 2p+1 if it requires 2p transverse cuts to render it simply connected. So he spoke of closed surfaces of connectivity 2p+1, rather than surfaces of genus p. (He showed an even number of cuts is required.) Then he shows a surface of connectivity 2p+_1 has p independent global holomorphic differentials, and discusses their moduli of periodicity. So if Clebsch introduced the terminology "genus", it seems the letter p preceded the term. The letter p may go back before Riemann. ?? | |
| Apr 1, 2012 at 17:18 | comment | added | Igor Rivin | род is a literal translation of "genus" | |
| Apr 1, 2012 at 17:05 | comment | added | YangMills | Thanks a lot, Martin. I found the reference of Clebsch (Crelle 63 (1864), 189-243) and it's freely available here gdz.sub.uni-goettingen.de/dms/load/img/… The letter $p$ appears first at the bottom of page 190, and see then formula (4) on page 192. It seems to come from terminology from theta functions. Can anybody fluent in German understand more precisely where the $p$ comes from? | |
| Apr 1, 2012 at 16:51 | comment | added | Mariano Suárez-Álvarez | What does род mean? | |
| Apr 1, 2012 at 16:32 | comment | added | Igor Rivin | I don't think that the russians made that big a contribution to anything having to do with genus in the 19th century, so probably german is the place to look... | |
| Apr 1, 2012 at 16:21 | comment | added | KConrad | The Russian word for genus is род (=rod in Latin letters), so p makes a lot of sense from that point of view. Or maybe it stands for plurigenus. :) | |
| Apr 1, 2012 at 15:10 | comment | added | Martin Brandenburg | According to jeff560.tripod.com/g.html, the earliest known use of "genus" was in the paper "Über die Anwendung der Abelschen Funktionen in der Geometrie" by A. Clebsh, published in 1863. Perhaps you can look there. | |
| Apr 1, 2012 at 14:50 | history | asked | YangMills | CC BY-SA 3.0 |