Abelian varieties, surfaces of general type and integrable systems.
Geometric study of a family of integrable systems. (Étude géométrique d'une famille de systémes intégrables.)
Abelian surfaces and Kowalewski's top
On the integrability of the generalized Yang-Mills system
We consider a hamiltonian system which, in a special case and under the gauge group SU(2), can be considered as a reduction of the Yang-Mills field equations. We prove explicitly, using the Lax spectral curve technique and the van Moerbeke-Mumford method, that the flows generated by the constants of motion are straight lines on the Jacobi variety of a genus two Riemann surface.
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