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
Abstract
Let be a (possibly ramified) cover, with X and Y of strictly positive genus. We develop tools to identify the Prym variety of , up to isogeny, as the Jacobian of a quotient curve C of the Galois closure of a composition of with a well-chosen map that identifies branch points of . 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 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
让是一个(可能分支的)覆盖层,其中X和Y属于严格正属。我们开发工具来识别 Prym 品种, 直到同源,作为组合的伽罗华闭包的商曲线C的雅可比行列式的精心挑选的地图标识的分支点. 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。