Jacobian variety of generalized Fermat curves
Quarterly Journal of Mathematics
| dc.creator | Carvacho, Mariela | |
| dc.creator | Hidalgo-Ortega, Rubén Antonio | |
| dc.creator | Quispe, Saúl | |
| dc.date | 2021-08-23T22:53:18Z | |
| dc.date | 2022-07-08T20:37:34Z | |
| dc.date | 2021-08-23T22:53:18Z | |
| dc.date | 2022-07-08T20:37:34Z | |
| dc.date | 2016 | |
| dc.date.accessioned | 2023-08-22T22:33:44Z | |
| dc.date.available | 2023-08-22T22:33:44Z | |
| dc.identifier | 1150003 | |
| dc.identifier | 1150003 | |
| dc.identifier | https://hdl.handle.net/10533/251138 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/8347460 | |
| dc.description | The isogenous decomposition of the Jacobian variety of classical Fermat curve of prime degree p >= 5 has been obtained by Aoki using techniques of number theory, by Barraza and Rojas in terms of decompositions of the algebra of groups, and by Hidalgo and Rodriguez using Kani-Rosen results. In the last, it was seen that all factors in the isogenous decomposition are Jacobian varieties of certain cyclic p-gonal curves. The highest Abelian branched covers of an orbifold of genus 0 with exactly n + 1 branch points, each one of order p, are provided by the so-called generalized Fermat curves of type (p, n) | |
| dc.description | these being a suitable fiber product of n-1 Fermat curves of degree p. In this paper, we provide a decomposition, up to isogeny, of the Jacobian variety of a generalized Fermat curve S of type (p, n) as a product of Jacobian varieties of certain cyclic p-gonal curves, whose explicit equations are provided in terms of the equations for S. As a consequence of this decomposition, we are able to provide explicit positive-dimensional families of closed Riemann surfaces whose Jacobian variety is isogenous to the product of elliptic curves. KeyWords Plus:GENUS 2 | |
| dc.description | AUTOMORPHISMS | |
| dc.description | PRODUCT | |
| 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/10.1093/qmath/haw009 | |
| 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 | Jacobian variety of generalized Fermat curves | |
| dc.title | Quarterly Journal of Mathematics | |
| dc.type | Articulo | |
| dc.type | info:eu-repo/semantics/publishedVersion |