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Hitchin Systems on Hyperelliptic Curves

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Abstract

We describe a class of spectral curves and find explicit formulas for the Darboux coordinates of Hitchin systems corresponding to classical simple groups on hyperelliptic curves. We consider in detail the systems with rank \(2\) groups on genus \(2\) curves.

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Acknowledgments

The authors are grateful to I. A. Taimanov for the discussion of Prymians of singular curves, although this question turned out to be beyond the scope of the final text. Among the works that significantly influenced the present study, we feel obliged to mention [10, 12, 8].

Funding

The work of the second author was supported by the Russian Foundation for Basic Research (project no. 20-01-00157) and by the RAS Program “Nonlinear Dynamics: Fundamental Problems and Applications.”

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Authors and Affiliations

  1. Faculty of Computer Science, National Research University Higher School of Economics, Pokrovskii bul. 11, Moscow, 109028, Russia

    P. I. Borisova

  2. Skolkovo Institute of Science and Technology, Bol’shoi bul. 30, str. 1, Moscow, 121205, Russia

    P. I. Borisova

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

    O. K. Sheinman

Authors
  1. P. I. Borisova
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  2. O. K. Sheinman
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Corresponding author

Correspondence to P. I. Borisova.

Additional information

Dedicated to A. G. Sergeev on the occasion of his 70th birthday

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Borisova, P.I., Sheinman, O.K. Hitchin Systems on Hyperelliptic Curves. Proc. Steklov Inst. Math. 311, 22–35 (2020). https://doi.org/10.1134/S0081543820060036

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  • DOI: https://doi.org/10.1134/S0081543820060036

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