Jacobian variety of generalized Fermat curves
Author
Carvacho, MarielaHidalgo-Ortega, Rubén Antonio
Quispe, Saúl
Abstract
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 ...
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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)
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Contest
Concurso Nacional Regular 2015Date de publicación
2016Journal title
Quarterly Journal of Mathematics