Kowalevski top and genus-2 curves

Kowalevski's curve of genus 2 is related to two other curves arising from t he solution of the Kowalevski top by the method of spectral curves in the c ase when the angular momentum of the top is orthogonal to the gravity vecto r. One is the Bobenko-Reyman-Semenov-Tian-Shansky curve of genus 2, the oth er is the spectral curve of the Kuznetsov-Tsiganov Lax matrix, of genus 3. The relations between the curves are given by correspondences, that is, mul tivalued maps, inducing isogenies of the corresponding Jacobian or Prym var ieties.