2000/11/29 by Rui Loja Fernandes, Fernandes, Rui Loja, Pol Vanhaecke +1
Mathematics · Physics and Astronomy · #35Q58 #37J35 #58J72 #70H06 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math-ph #math.AG #math.MP #msc:35Q58 #msc:37J35 #msc:58J72 #msc:70H06 #nlin.SI
paper · pdf · doi:10.48550/arxiv.math-ph/0011051
Final version. To appear in CMP
openalex publication_date 2000/11/29 · arxiv created 2001/03/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ai=ai(ai-1-ai+1), i=1,...,n, an+1=a1, 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.