Abstract:
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
is an affine part of a hyperelliptic Prym variety, obtained by removing n translates of the theta divisor, and we conclude that this integrable system is algebraic completely integrable.
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Received: 12 December 2000 / Accepted: 26 March 2001
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Fernandes, R., Vanhaecke, P. Hyperelliptic Prym Varieties and Integrable Systems. Commun. Math. Phys. 221, 169–196 (2001). https://doi.org/10.1007/s002200100476
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DOI: https://doi.org/10.1007/s002200100476