Superintegrable systems and Riemann-Roch theorem

Abstract

In algebraic geometry, there is a reduction algorithm that transforms the unreduced divisor into a unique reduced divisor, which existence is guaranteed by the Riemann-Roch theorem. We discuss application of this algorithm to construction of finite-dimensional superintegrable systems with $n$ degrees of freedom identifying coordinates of the reduced divisor with integrals of motion.

LaTeX with AMS packages, 15 pages

References in corpus (8)

• On maximally superintegrable systems
• On algebraic construction of certain integrable and super-integrable systems
• Leonard Euler: addition theorems and superintegrable systems
• Addition theorems and the Drach superintegrable systems
• Elliptic curve arithmetic and superintegrable systems
• The Kepler problem: polynomial algebra of non-polynomial first integrals
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Cited by in corpus (5)

• Superintegrability of Calogero-Moser systems associated with the cyclic quiver
• Reducible Abelian varieties and Lax matrices for Euler's problem of two fixed centres
• Reduction of divisors and Clebsch system
• Reduction of divisors for classical superintegrable $GL(3)$ magnetic chain
• On two-dimensional Hamiltonian systems with sixth-order integrals of motion