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  • 9 - The Periodic 6-Particle Kac-van Moerbeke System

  • Edited by Ron Donagi, University of Pennsylvania, Tony Shaska, Oakland University, Michigan
  • Book:
    Integrable Systems and Algebraic Geometry
    Published online:
    19 March 2020
    Print publication:
    02 April 2020, pp 192-216

  • Summary

    We study some algebraic-geometrical aspects of the periodic 6-particle Kac–van Moerbeke system. This system is known to be algebraically integrable, having the affine part of a hyperelliptic Jacobian of a genus two curve as the generic fiber of its momentum map. Particular attention goes to the divisor needed to complete this fiber into an Abelian variety: it consists of six copies of the curve, intersecting according to a pattern which we will determine. We will also compare this divisor to the divisor that appears in some natural singular compactification of the fiber.