Division polynomials and canonical local heights on hyperelliptic Jacobians
Division polynomials and canonical local heights on hyperelliptic Jacobians
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DOI：
10.1007/s00229-010-0394-9
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发表时间：
2011-03
影响因子：
0.6
通讯作者：
Y. Uchida
中科院分区：
文献类型：
--
作者：
Y. Uchida
将椭圆曲线的除多项式推广到复数域上的超椭圆雅可比算子。我们通过使用超椭圆sigma函数来构造它们。利用除多项式，我们描述了雅可比矩阵上的一点是扭点的条件。证明了除多项式的行列式表达式和递推公式等性质。我们还研究了sigma函数、除法多项式和正则局部高度函数之间的关系。
We generalize the division polynomials of elliptic curves to hyperelliptic Jacobians over the complex numbers. We construct them by using the hyperelliptic sigma function. Using the division polynomial, we describe a condition that a point on the Jacobian is a torsion point. We prove several properties of the division polynomials such as determinantal expressions and recurrence formulas. We also study relations among the sigma function, the division polynomials, and the canonical local height functions.