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Hyperelliptic Prym Varieties and Integrable Systems

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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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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal.¶e-mail: rfern@math.ist.utl.pt, , , , , , PT

    Rui Loja Fernandes

  2. Université de Poitiers, Département de Mathématiques, Téléport 2, Boulevard Marie et Pierre Curie,¶BP 30179, 86962 Futuroscope Chasseneuil Cedex, France.¶E-mail: Pol.Vanhaecke@mathlabo.univ-Poitiers.fr, , , , , , FR

    Pol Vanhaecke

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  1. Rui Loja Fernandes
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  2. Pol Vanhaecke
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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

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