Genus 2 Curves with (3, 3)-Split Jacobian and Large Automorphism Group
Genus 2 Curves with (3, 3)-Split Jacobian and Large Automorphism Group
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具有 (3, 3) 分裂雅可比行列式和大自同构群的属 2 曲线
DOI：
10.1007/3-540-45455-1_17
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发表时间：
2002
影响因子：
0.5
通讯作者：
T. Shaska
中科院分区：
文献类型：
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作者：
T. Shaska
设C是定义在k上的亏格为2的曲线，char（k）=0.如果C有一个（3，3）-分裂雅可比矩阵，那么我们证明了自同构群Aut（C）同构于以下之一：Z2，V4，D8或D12。Aut（C）同构于D8的亏格为2的曲线C有6个C-同构类（分别为，D12）和（3，3）-分裂雅可比矩阵。我们证明，正是四个（分别，三个）具有组D8的这些类（分别，D12）具有在Q上定义的代表。我们详细讨论其中的一些曲线，并找到它们的合理点。
Let C be a genus 2 curve defined over k, char(k) =0. If C has a (3, 3)-split Jacobian then we show that the automorphism group Aut(C) is isomorphic to one of the following: Z2, V4, D8, or D12. There are exactly six C-isomorphism classes of genus two curves C with Aut(C) isomorphic to D8 (resp., D12) and with (3, 3)-split Jacobian. We show that exactly four (resp., three) of these classes with group D8 (resp., D12) have representatives defined over Q. We discuss some of these curves in detail and find their rational points.