Reduction of divisors and the Clebsch system. (English) Zbl 1490.37081
Summary: There are a few Lax matrices of the Clebsch system. Poles of the Baker-Akhiezer function determine the class of equivalent divisors on the corresponding spectral curves. According to the Riemann-Roch theorem, each class has a unique reduced representative. We discuss properties of such a reduced divisor on the spectral curve of \(3\times 3\) Lax matrix having a natural generalization to \(gl^*(n)\) case.
MSC:
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 70E15 | Free motion of a rigid body |
| 14H70 | Relationships between algebraic curves and integrable systems |
| 14D06 | Fibrations, degenerations in algebraic geometry |
| 58K10 | Monodromy on manifolds |
| 58K50 | Normal forms on manifolds |
| 70E05 | Motion of the gyroscope |
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