Geodesic
Spectral Curves of the Hyperelliptic Hitchin Systems
Funkcionalʹnyj analiz i ego priloženiâ, Tome 53 (2019) no. 4, pp. 63-78

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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. 
@article{FAA_2019_53_4_a5,
     author = {O. K. Sheinman},
     title = {Spectral {Curves} of the {Hyperelliptic} {Hitchin} {Systems}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {63--78},
     publisher = {mathdoc},
     volume = {53},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2019_53_4_a5/}
}
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O. K. Sheinman. Spectral Curves of the Hyperelliptic Hitchin Systems. Funkcionalʹnyj analiz i ego priloženiâ, Tome 53 (2019) no. 4, pp. 63-78. http://geodesic.mathdoc.fr/item/FAA_2019_53_4_a5/