Sato Grassmannian and Degenerate Sigma Function
Sato Grassmannian and Degenerate Sigma Function
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DOI：
10.1007/s00220-020-03704-5
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发表时间：
2020-02
影响因子：
2.4
通讯作者：
J. Bernatska;V. Enolski;A. Nakayashiki
中科院分区：
文献类型：
--
作者：
J. Bernatska;V. Enolski;A. Nakayashiki
研究了超椭圆sigma函数的退化性。我们使用Sato Grassmannian用于此目的。有理函数的简单分解给出了佐藤格拉斯曼框架的普吕克坐标的分解。然后给出了亏格超椭圆曲线退化所对应的τ函数的一个分解，并给出了亏格超椭圆曲线退化所对应的τ函数的一个项.由于τ函数是用σ函数描述的，我们得到了退化超椭圆σ函数的相应公式。
The degeneration of the hyperelliptic sigma function is studied. We use the Sato Grassmannian for this purpose. A simple decomposition of a rational function gives a decomposition of Plücker coordinates of a frame of the Sato Grassmannian. It then gives a decomposition of the tau function corresponding to the degeneration of a hyperelliptic curve of genusgin terms of the tau functions corresponding to a hyperelliptic curve of genus. Since the tau functions are described by sigma functions, we get the corresponding formula for the degenerate hyperelliptic sigma function.