Indonesian Journal of Mathematics and Applications
Vol. 2 No. 2 (2024): Indonesian Journal of Mathematics and Applications

Morphisms and Algebraic Points on the Quotients of the Fermat Quintic

Fall, Moussa (Unknown)



Article Info

Publish Date
25 Sep 2024

Abstract

The purpose of this paper is to determine morphisms and algebraic points of low degree on the quotients of the Fermat quintic. An algebraic point of degree at most $3$ is called an algebraic point of low degree. The quotients of the Fermat quintic is a family curves $\mathcal{C}_{rs}(5) : v^5 =u^r(u-1)^s$ where $r$ and $s$ are integers such that: $1< r, s, r+s< 5$. We determine explicitly the morphisms between the curves $\mathcal{C}_{rs}(5)$. By applying Abel Jacobi's theorem and using Riemann-Roch spaces, we give a parametrization of algebraic points of low degree on the special curve $\mathcal{C}_{1,1}(5)$. Birational morphisms allow us to determine the set of algebraic points of low degree on each curve of the family curves $\mathcal{C}_{rs}(5)$.

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Journal Info

Abbrev

ijma

Publisher

Subject

Computer Science & IT Education Mathematics Other

Description

The Indonesian Journal of Mathematics and Applications is a journal managed by Universitas Brawijaya, Malang, Indonesia, that is published twice a year (in March and September). IJMA is devoted to research articles of the highest quality in all areas of mathematics and its applications, statistics, ...