Two-coverings of Jacobians of curves of genus 2
Two-coverings of Jacobians of curves of genus 2
复制标题
属 2 曲线的雅可比行列式的两次覆盖
DOI：
10.1112/plms/pdr012
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发表时间：
2012
影响因子：
1.8
通讯作者：
Flynn E
中科院分区：
文献类型：
--
作者：
Flynn E
给定定义在不同于2的域特征上的具有Jacobian变量J的CurveCof亏格2，我们证明了对应于H1的一个大的子群的元素(Gal(ks/k)，J[2](Ks))(当kis是整体域时包含Selmer群)的双覆盖可以作为72个二次曲面的交集嵌入到ℙ15k中，就像JacobianJ本身一样.此外，我们实际上在一般情况下给出了这些扭曲模型的显式方程，推广了Gordon和Grant的工作，该工作仅适用于所有的魏尔斯特拉斯点都是有理的情况。此外，我们还描述了雅可比方程本身，并回答了Cassel和Flynn关于从ℙ3中的Kummer曲面到ℙ5中去奇异的Kummer曲面的映射的问题。
Given a curveCof genus 2 defined over a fieldkof characteristic different from 2, with a Jacobian varietyJ, we show that the two‐coverings corresponding to elements of a large subgroup of H1(Gal(ks/k),J[2](ks)) (containing the Selmer group whenkis a global field) can be embedded as an intersection of 72 quadrics in ℙ15k, just as the JacobianJitself. Moreover, we actually give explicit equations for the models of these twists in the generic case, extending the work of Gordon and Grant which applied only to the case when all Weierstrass points are rational. In addition, we describe elegant equations of the Jacobian itself, and answer a question of Cassels and Flynn concerning a map from the Kummer surface in ℙ3to the desingularized Kummer surface in ℙ5.