A shortcut to the Kovalevskaya curve
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Abstract
We present a systematic way of derivation of the algebraic curves of separation of variables for the classical Kovalevskaya top and its generalizations, starting from the spectral curve of the corresponding Lax representation found by Reyman and Semonov-Tian-Shansky. In particular, we show how the known Kovalevskaya curve of separation can be obtained, by a simple one-step transformation, from the spectral curve. The algorithm works for the general constants of motion of the system and is based on W. Barth's description of Prym varieties via pencils of genus 3 curves. It also allows us to derive new curves of separation of variables in various generalizations of this system.Keywords
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This publication has 19 references indexed in Scilit:
- Jacobiennes des courbes spectrales et systèmes hamiltoniens complètement intégrablesActa Mathematica, 1990
- The full Geometry of Kowalewski's top and (1, 2)‐abelian surfacesCommunications on Pure and Applied Mathematics, 1989
- The Kowalewski top 99 years later: A Lax pair, generalizations and explicit solutionsCommunications in Mathematical Physics, 1989
- The Kowalewski and Hénon-Heiles motions as Manakov geodesic flows onSO(4) — a two-dimensional family of Lax pairsCommunications in Mathematical Physics, 1988
- Lax representation with a spectral parameter for the Kowalewski top and its generalizationsLetters in Mathematical Physics, 1987
- Equivalent problems in rigid body dynamics?IICelestial Mechanics and Dynamical Astronomy, 1987
- The intersection of four quadrics in ℙ6, abelian surfaces and their moduliMathematische Annalen, 1987
- Prym varieties and the geodesic flow onSO(n)Mathematische Annalen, 1986
- Geometry of Algebraic Curves1985
- Prym varieties and the Schottky problemInventiones Mathematicae, 1977