A shortcut to the Kovalevskaya curve

There have already been numerous studies and interpretations of the famous separation of variables in the integrable top of S. Kovalevskaya. In this talk we show how the original Kovalevskaya curve of separation can be obtained, by a simple one-step transformation, from the spectral curve of the Lax representation found by Bobenko, Reyman, and Semenov-Tian-Shansky. The algorithm works for the general constants of motion of the top and is based on W. Barth's description of Prym varieties via pencils of genus 3 curves. This also allows us to derive existing and new curves of separation for the Kovalevskaya gyrostat in one and two force fields.Non UBCUnreviewedAuthor affiliation: Universitat Politechnica de CatalunyaFacult