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In this paper, a finite dimensional algebraic completely integrable system
is considered. We show that the intersection of levels of integrals
completes into an abelian surface (a two dimensional complex algebraic
torus) of polarization $\left( 2,8\right) $ and that the flow of the system
can be linearized on it.
70H06, 37J35, 14H70, 14K20
Integrable systems, curves, abelian varieties