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Reduction of Divisors and the Clebsch System

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Abstract

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.

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Funding

The work of A. V. Tsiganov was supported by the Russian Science Foundation (project no. 19-71-30012) and performed at the Steklov Mathematical Institute of the Russian Academy of Sciences.

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  1. Steklov Mathematical Institute of Russian Academy of Sciences , ul. Gubkina 8, 119991, Moscow, Russia

    Andrey V. Tsiganov

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  1. Andrey V. Tsiganov
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Correspondence to Andrey V. Tsiganov.

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Dedicated to the memory of Alexey V. Borisov

MSC2010

14D06, 37J35, 58K10, 58K50, 70E15

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Tsiganov, A.V. Reduction of Divisors and the Clebsch System. Regul. Chaot. Dyn. 27, 307–319 (2022). https://doi.org/10.1134/S1560354722030030

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