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Hyperelliptic Prym Varieties and Integrable Systems | | Rui Loja Fernandes
; Pol Vanhaecke
; | | Date: |
29 Nov 2000 | | Subject: | Mathematical Physics; Algebraic Geometry; Exactly Solvable and Integrable Systems MSC-class: 35Q58, 37J35, 58J72, 70H06 | math-ph math.AG math.MP nlin.SI | | 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 generic fiber of the momentum map of the periodic Volterra lattice $$dot a_i=a_i(a_{i-1}-a_{i+1}), qquad i=1,...,n,quad a_{n+1}=a_1,$$ 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. | | Source: | arXiv, math-ph/0011051 | | Services: | Forum | Review | PDF | Favorites | |
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