O. K. Sheinman, “Spectral Curves of the Hyperelliptic Hitchin Systems”, Funktsional. Anal. i Prilozhen., 53:4 (2019), 63–78; Funct. Anal. Appl., 53:4 (2019), 291

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Funktsional'nyi Analiz i ego Prilozheniya, 2019, Volume 53, Issue 4, Pages 63–78
DOI: https://doi.org/10.4213/faa3648 (Mi faa3648)

This article is cited in 7 scientific papers (total in 7 papers)

Spectral Curves of the Hyperelliptic Hitchin Systems

O. K. Sheinman

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Full-text PDF (347 kB) Citations (7)

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DOI: https://doi.org/10.4213/faa3648

Abstract: This paper describes a class of spectral curves and gives explicit formulas for the Darboux coordinates of the Hitchin systems of types

$A_l$ ,

$B_l$ , and

$C_l$ on hyperelliptic curves. The current state of the problem in the case of the systems of type

$D_l$ is described.

Received: 26.01.2019
Revised: 27.05.2019
Accepted: 08.08.2019

English version:
Functional Analysis and Its Applications, 2019, Volume 53, Issue 4, Pages 291–303
DOI: https://doi.org/10.1134/S0016266319040063

Bibliographic databases:

Document Type: Article

UDC: 514.8

Language: Russian

Citation: O. K. Sheinman, “Spectral Curves of the Hyperelliptic Hitchin Systems”, Funktsional. Anal. i Prilozhen., 53:4 (2019), 63–78; Funct. Anal. Appl., 53:4 (2019), 291–303

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/faa3648

https://doi.org/10.4213/faa3648

https://www.mathnet.ru/eng/faa/v53/i4/p63

This publication is cited in the following 7 articles:

Russian Math. Surveys, 79:4 (2024), 683–720
O. K. Sheinman, “Separation of Variables for Hitchin Systems with the Structure Group $\mathrm {SO}(4)$ on Genus $2$ Curves”, Proc. Steklov Inst. Math., 325 (2024), 292–303
P. Borisova, “Separation of variables for type $D_n$ Hitchin systems on a hyperelliptic curve”, Russian Math. Surveys, 76:2 (2021), 363–365
P. I. Borisova, O. K. Sheinman, “Hitchin Systems on Hyperelliptic Curves”, Proc. Steklov Inst. Math., 311 (2020), 22–35
O. K. Sheinman, “Quantization of integrable systems with spectral parameter on a Riemann surface”, Dokl. Math., 102:3 (2020), 524–527
O. K. Sheinman, “Spectral Curves of the Hyperelliptic Hitchin Systems”, Funct. Anal. Appl., 53:4 (2019), 291–303
O. K. Sheinman, “Integrable Systems of Algebraic Origin and Separation of Variables”, Funct. Anal. Appl., 52:4 (2018), 316–320

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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Abstract page:	436
Full-text PDF :	117
References:	60
First page:	6

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