The complex geometry of an integrable system

 

Ahmed LESFARI

Address.
Department of Mathematics, Faculty of Sciences
University of Chouaib Doukkali
B.P. 20, El-Jadida, Morocco

E-mail:  lesfari@ucd.ac.ma   lesfariahmed@yahoo.fr

Abstract.
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.

AMSclassification.
70H06, 37J35, 14H70, 14K20

Keywords.
Integrable systems, curves, abelian varieties