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Stratifications of hyperelliptic Jacobians and the Sato Grassmannian. (English) Zbl 0827.14015
Summary: A one-dimensional family of stratifications on a hyperelliptic Jacobian is introduced. It generalizes a well-known stratification, considered in algebraic geometry, in the context of special divisors. The stratification is shown to be related to a natural stratification on the Sato Grassmannian, via an extension of Krichever’s map. It is also related to the stratification associated to the Laurent solutions of certain vector fields which can both be seen as living on the Grassmannian or on the Jacobian.

MSC:
14H40 Jacobians, Prym varieties
14M15 Grassmannians, Schubert varieties, flag manifolds
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.)
58A35 Stratified sets
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