Field of moduli of generalized Fermat curves of type (k, 3) with an application to non-hyperelliptic dessins d'enfants
Journal of Symbolic Computation
| dc.creator | Hidalgo-Ortega, Rubén Antonio | |
| dc.creator | Johnson, Pilar | |
| dc.date | 2021-08-23T22:55:13Z | |
| dc.date | 2022-07-07T02:31:29Z | |
| dc.date | 2021-08-23T22:55:13Z | |
| dc.date | 2022-07-07T02:31:29Z | |
| dc.date | 2015 | |
| dc.date.accessioned | 2023-08-22T06:44:05Z | |
| dc.date.available | 2023-08-22T06:44:05Z | |
| dc.identifier | 1150003 | |
| dc.identifier | 1150003 | |
| dc.identifier | https://hdl.handle.net/10533/251582 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/8329032 | |
| dc.description | A generalized Fermat curve of type (k, 3), where k >= 2, is a closed Riemann surface admitting a group H congruent to Z(k)(3) as a group of conformal automorphisms so that the quotient orbifold S / H is the Riemann sphere and it has exactly 4 cone points, each one of order k. Every genus one Riemann surface is a generalized Fermat curve of type (2, 3) and, if k >= 3, then a generalized Fermat curve of type (k, 3) is non-hyperelliptic. For each generalized Fermat curve, we compute its field of moduli and note that it is a field of definition. Moreover, for k = e(2i pi/P), where p >= 5 is a prime integer, we produce explicit algebraic models over the corresponding field of moduli. As a byproduct, we observe that the absolute Galois group Gal((Q) over bar /Q) acts faithfully at the level of non-hyperelliptic dessins d'enfants. This last fact was already known for dessins of genus 0, 1 and for hyperelliptic ones, but it seems that the non-hyperelliptic situation is not explicitly given in the existent literature. (C) 2014 Elsevier Ltd. All rights reserved. | |
| dc.description | Regular 2015 | |
| dc.description | FONDECYT | |
| dc.description | FONDECYT | |
| dc.language | eng | |
| dc.relation | handle/10533/111557 | |
| dc.relation | handle/10533/111541 | |
| dc.relation | handle/10533/108045 | |
| dc.relation | https://doi.org/10.1016/j.jsc.2014.09.042 | |
| dc.rights | Atribución-NoComercial-SinDerivadas 3.0 Chile | |
| dc.rights | http://creativecommons.org/licenses/by-nc-nd/3.0/cl/ | |
| dc.rights | info:eu-repo/semantics/article | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.title | Field of moduli of generalized Fermat curves of type (k, 3) with an application to non-hyperelliptic dessins d'enfants | |
| dc.title | Journal of Symbolic Computation | |
| dc.type | Articulo | |
| dc.type | info:eu-repo/semantics/publishedVersion |