Hyperelliptic Prym Varieties and Integrable Systems
Copyright policy )Hyperelliptic Prym Varieties and Integrable Systems
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.
Final version. To appear in CMP
- Instituto Superior de Espinho Portugal
- University of Poitiers France
- University of Poitiers France
algebraic completely integrable systems, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, periodic Volterra lattice, Nonlinear Sciences - Exactly Solvable and Integrable Systems, 35Q58, 37J35, 58J72, 70H06, FOS: Physical sciences, hyperelliptic Prym systems, Mathematical Physics (math-ph), Mathematics - Algebraic Geometry, momentum map, FOS: Mathematics, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions, Relationships between algebraic curves and integrable systems, Jacobians, Prym varieties, Exactly Solvable and Integrable Systems (nlin.SI), Algebraic Geometry (math.AG), Mathematical Physics
algebraic completely integrable systems, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, periodic Volterra lattice, Nonlinear Sciences - Exactly Solvable and Integrable Systems, 35Q58, 37J35, 58J72, 70H06, FOS: Physical sciences, hyperelliptic Prym systems, Mathematical Physics (math-ph), Mathematics - Algebraic Geometry, momentum map, FOS: Mathematics, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions, Relationships between algebraic curves and integrable systems, Jacobians, Prym varieties, Exactly Solvable and Integrable Systems (nlin.SI), Algebraic Geometry (math.AG), Mathematical Physics
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