The elliptic Calogero-Moser integrable system for an arbitrary root system has a realization as a moduli space of Higgs bundles over an Abelian variety associated with the elliptic curve and with the root system. This paper examines the Fourier-Mukai transform of this, giving an interpretation of the system on a network of elliptic curves. The rational and trigonometric versions of the systems are briefly discussed, and it is shown how they enter as degenerations in this geometric context.
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Research Article| June 26 2018
Geometry of Calogero-Moser systems
Special Collection: In Memory of Ludwig Faddeev
Indranil Biswas, Jacques Hurtubise; Geometry of Calogero-Moser systems. J. Math. Phys. 1 September 2018; 59 (9): 091403. https://doi.org/10.1063/1.5030863
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