Hyperelliptic Prym Varieties and Integrable Systems
Hyperelliptic Prym Varieties and Integrable Systems
复制标题
超椭圆 Prym 品种和可积系统
DOI：
10.1007/s002200100476
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发表时间：
2000
影响因子：
2.4
通讯作者：
P. Vanhaecke
中科院分区：
文献类型：
--
作者：
R. Fernandes;P. Vanhaecke
我们引入 Mumford 系统的两个代数完全可积类似物，我们称之为超椭圆 Prym 系统，因为每个超椭圆 Prym 簇都表现为其动量图的纤维。 作为一个应用，我们展示了周期性 Volterra 格子\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} 动量图的一般纤维\begin{document}\end{document} 是超椭圆 Prym 簇的仿射部分，通过去除 theta 除数的 n 平移而获得，我们得出结论，该可积系统是代数完全可积的。
We introduce two algebraic completely integrable analogues of the Mumford systems which we call hyperelliptic Prym systems, because every hyperelliptic Prym variety appears as a fiber of their momentum map. As an application we show that the general fiber of the momentum map of the periodic Volterra lattice\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} is an affine part of a hyperelliptic Prym variety, obtained by removingntranslates of the theta divisor, and we conclude that this integrable system is algebraic completely integrable.