Large torsion subgroups of split Jacobians of curves of genus two or three
Large torsion subgroups of split Jacobians of curves of genus two or three
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二、三亏格曲线分裂雅克比行列式的大扭转子群
DOI：
10.1515/form.2000.008
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发表时间：
1998
影响因子：
0.8
通讯作者：
B. Poonen
中科院分区：
文献类型：
--
作者：
Everett W. Howe;Franck Leprévost;B. Poonen
我们构造了Q上亏格为2或3的曲线族的例子，这些曲线族的雅可比数完全分裂并且具有各种大的有理挠子群。例如，P^1上某个正秩参数椭圆曲面上的有理点是Q上一族亏格为2的曲线，它们的雅可比矩阵各有128个有理扭点。另外，我们还发现亏格3曲线15625（X^4 + Y^4 + Z^4）- 96914（X^2Y^2 + X^2Z^2 + Y^2Z^2）= 0，其雅可比矩阵有864个有理挠点.
这篇论文发表在Forum Math.12（2000）315-364。
We construct examples of families of curves of genus 2 or 3 over Q whose Jacobians split completely and have various large rational torsion subgroups. For example, the rational points on a certain elliptic surface over P^1 of positive rank parameterize a family of genus-2 curves over Q whose Jacobians each have 128 rational torsion points. Also, we find the genus-3 curve 15625(X^4 + Y^4 + Z^4) - 96914(X^2 Y^2 + X^2 Z^2 + Y^2 Z^2) = 0, whose Jacobian has 864 rational torsion points.
This paper has appeared in Forum Math. 12 (2000) 315-364.