Addition in Jacobians of hyperelliptic curves and the periodic discrete Toda lattice

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Addition in Jacobians of hyperelliptic curves and the periodic discrete Toda lattice

フォーマット:
雑誌論文
Kyushu Univ. Production 九州大学成果文献
責任表示:
野邊, 厚(千葉大学教育学部)
Nobe, Atsushi(Faculty of Education, Chiba University)
本文言語:
英語
出版情報:
応用力学研究所研究集会報告. 23AO-S7, (12), pp. 84-89, 2012-03. 九州大学応用力学研究所
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Publisher
概要:
We give a geometric realization of the (g+1)-periodic discrete Toda lattice. The realization is given as the addition of g-tuples of points on the hyperelliptic curve of genus g, which is the spectral curve of the (g+1)-periodic discrete Toda lattice. We show that the addition on the hyperelliptic curve is induced from its Jacobian through a surjection and is realized by using the intersection of the hyperelliptic curve and a curve of genus 0.
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