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Jacobiennes des courbes spectrales et systèmes hamiltoniens complètement intégrables. (The Jacobians of spectral curves and completely integrable Hamiltonian systems). (French) Zbl 0712.58031
The author gives a geometric interpretation of the Mumford construction for the hyperelliptic Jacobians. This enables him to point out some new integrable Hamiltonian mechanical systems.
Reviewer: M.Puta

MSC:
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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[1] Artin, M., On Azumaya algebras and finite-dimensional representations of rings.J. Algebra, 11 (1969), 532–563. · Zbl 0222.16007
[2] Adler, M. &van Moerbeke, P., Completely integrable systems, Euclidean Lie algebras and curves; linearization of Hamiltonian systems, Jacobi varieties and representation theory.Adv. in Math., 38 (1980), 267–379. · Zbl 0455.58017
[3] Beauville, A., Narasimhan, M. S. &Ramanan, S., Spectral curves and generalised theta divisor.J. Reine Angew. Math., 398 (1989), 169–179. · Zbl 0666.14015
[4] Formanek, E., The center of the ring of 3{\(\times\)}3 generic matrices.Linear and Multilinear Algebra, 7 (1979), 203–212. · Zbl 0419.16010
[5] –, The center of the ring of 4{\(\times\)}4 generic matrices.J. Algebra, 62 (1980), 304–319. · Zbl 0437.16013
[6] Kempf, G., The equations defining a curve of genus 4.Proc. Amer. Math. Soc., 97 (1986), 214–225. · Zbl 0595.14021
[7] Le Bruyn, L., Some remarks on rational matrix invariants.J. Algebra, 118 (1988), 487–493. · Zbl 0668.14032
[8] Maruyama, M., The equations of plane curves and the moduli space of vector bundles onP 2.Algebraic and Topological Theory (to the memory of T. Miyata), 430–466 (1985).
[9] Mumford, D. &Fogarty, J.,Geometric Invariant Theory. 2nd edition Ergebnisse der Math. 34, Springer Verlag, Berlin-Heidelberg-New York (1982). · Zbl 0504.14008
[10] Mumford, D.,Tata lectures on Theta II. Progress in Math. 43. Birkhäuser, Boston-Basel-Stuttgart (1984). · Zbl 0549.14014
[11] Weinstein, A., The local structure of Poisson manifolds.J. Differential Geom., 18 (1983), 523–557. · Zbl 0524.58011
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