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

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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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登録日 2012.07.27
更新日 2015.12.07