Addition in Jacobians of hyperelliptic curves and the periodic discrete Toda lattice
Nobe, Atsushi(Faculty of Education, Chiba University)
- 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
- 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.