Timeline for Configuration of the branch locus of a branched covering of an elliptic curve
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 7, 2013 at 23:19 | review | Suggested edits | |||
| Aug 7, 2013 at 23:34 | |||||
| Sep 12, 2012 at 16:23 | vote | accept | Sofia | ||
| Sep 12, 2012 at 11:20 | answer | added | Peter Mueller | timeline score: 2 | |
| Sep 12, 2012 at 8:46 | answer | added | Francesco Polizzi | timeline score: 3 | |
| Sep 11, 2012 at 14:49 | comment | added | Sofia | Thank you very much for the information. Still I do not get how I can exclude some configuration of $B$. For example I would like to see if the ramification divisor can be supported on one point The ramification supported on 1 point implies that the branched divisor is supported on one point and whose counter image is a quintuple point. With the info I have I find it difficult to see, for example, if there exist or not an $n\ge 5$ such that $S_n$ has a prim. trans. subgroup generated by 3 elements $a,b,g$ with $g$ a 5-cycle and [ab]g=e$. Being the base elliptic I do not have info on $n$... | |
| Sep 11, 2012 at 11:44 | comment | added | Peter Mueller | Look e.g. at en.wikipedia.org/wiki/Riemann-Hurwitz_formula. The ramification indices $e_P$ there are the cycle lengths appearing in the permutations $g_i$. | |
| Sep 11, 2012 at 11:19 | comment | added | Sofia | Ok! Now I understand why it seemed to me I had to few conditions. Which condition do I need to add? Might them be, for example, if $B$ has cardinality 1 - $g^2=1$ if over $B$ I have two double points? - $g^5=1$ if over $B$ I have one quintuple point? Could you give me example/references. Mine just explain how to recover Hurwitz formula and it is kind of useless in my case. | |
| Sep 11, 2012 at 9:10 | comment | added | Peter Mueller | Your tuples of permutations indeed describe coverings of an elliptic curve with branch locus of size $3$, $2$, or $1$, respectively. However, the requirement that the curve $C$ has genus $3$ puts further restrictions on the elements $g_i$ (via Riemann-Hurwitz). | |
| Sep 11, 2012 at 8:25 | history | asked | Sofia | CC BY-SA 3.0 |