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Jacobians of singular spectral curves and completely integrable systems

Published online by Cambridge University Press:  20 January 2009

Olivier Vivolo
Olivier Vivolo
Affiliation:
Laboratoire Emile Picard, URA CNRS 5580, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex, France (vivolo@picard.ups-tlse.fr)
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Abstract

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Consider an isospectral manifold formed by matrices M ∈ glr(ℂ)[x] with a fixed leading term. The description of such a manifold is well known in the case of a diagonal leading term with different eigenvalues. On the other hand, there are many important systems where this term has multiple eigenvalues. One approach is to impose conditions in the sub-leading term. The result is that the isospectral set is a smooth manifold, bi-holomorphic to a Zariski open subset of the generalized Jacobian of a singular curve.

Keywords

integrabilityJacobian variety
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 3 , October 2000 , pp. 605 - 623
Copyright
Copyright © Edinburgh Mathematical Society 2000

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