Kowalevski top and genus-2 curves (Q2716880)

The author, mainly using techniques developed by himself and \textit{F. Leprévost} in [J. Reine Angew. Math. 514, 103-111 (1999; Zbl 0961.11021)], shows the correpondences between the Bobenko-Reyman-Semenov-Tian-Shansky curve of genus \(2\), and the spectral curve of the Kuznetsov-Tsiganov Lax matrix of genus \(3\). Both curves are closely related to Kowalewski's curve of genus \(2\), arising from the solution of the Kowalewski top by the method of spectral curves in the case when the angular momentum of the top is orthogonal to the gravity vector.