Reduction of divisors and Clebsch system

Abstract

There are a few Lax matrices of the Clebsch system. Poles of the Baker-Akhiezer function determine the class of equivalent divisors on the corresponding spectral curves. According to the Riemann-Roch theorem, each class has a unique reduced representative. We discuss properties of such reduced divisor on the spectral curve of $3\times 3$ Lax matrix having a natural generalization to $g{l}^{\ast }(n)$ case.

arXiv comment14 pages, no figures, LaTeX with AMS fonts

References in corpus (14)

• On integrability of Hirota-Kimura type discretizations
• Separation of Variables in the Elliptic Gaudin Model
• On auto and hetero Backlund transformations for the Henon-Heiles systems
• Superintegrable systems and Riemann-Roch theorem
• The Clebsch System
• A complete and explicit solution to the three-dimensional problem of two fixed centres
• On integration of the Kowalevski gyrostat and the Clebsch problems
• Discretization and superintegrability all rolled into one
• Reduction of divisors for classical superintegrable $GL(3)$ magnetic chain
• A new approach to separation of variables for the Clebsch integrable system. Part II: Inversion of the Abel--Prym map
• A new approach to separation of variables for the Clebsch integrable system. Part I: Reduction to quadratures
• Reducible Abelian varieties and Lax matrices for Euler's problem of two fixed centres
• A note on elliptic coordinates on the Lie algebra e(3)
• Reduction of divisors and Kowalevski top

Cited by in corpus (2)

• On tensor invariants of the Clebsch system
• Reduction of divisors and Kowalevski top