当前位置: X-MOL 学术Exp. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Decomposing Jacobians Via Galois covers
Experimental Mathematics ( IF 0.5 ) Pub Date : 2021-07-09 , DOI: 10.1080/10586458.2021.1926008
Davide Lombardo 1 , Elisa Lorenzo García 2 , Christophe Ritzenthaler 2 , Jeroen Sijsling 3
Affiliation  

Abstract

Let ϕ:XY be a (possibly ramified) cover, with X and Y of strictly positive genus. We develop tools to identify the Prym variety of ϕ, up to isogeny, as the Jacobian of a quotient curve C of the Galois closure of a composition XYP 1 of ϕ with a well-chosen map YP 1 that identifies branch points of ϕ. To our knowledge, this method recovers all previously obtained descriptions of Prym varieties as Jacobians. It also finds new decompositions, and for some of these, including one where X has genus 3, Y has genus 1 and ϕ is a degree 3 map totally ramified over 2 points, we find an algebraic equation of the curve C.



中文翻译:

通过伽罗华分解雅可比行列

摘要

φ:X是一个(可能分支的)覆盖层,其中XY属于严格正属。我们开发工具来识别 Prym 品种φ, 直到同源,作为组合的伽罗华闭包的商曲线C的雅可比行列式XP 1个φ精心挑选的地图P 1个标识的分支点φ. 据我们所知,该方法恢复了所有先前获得的 Prym 簇描述为雅可比矩阵。它还会找到新的分解,对于其中的一些分解,包括X的亏格为 3、Y 的亏格为 1 和φ是完全分叉 2 个点的 3 阶映射,我们找到曲线C的代数方程。

更新日期:2021-07-09
down
wechat
bug