Stratifications of Hyperelliptic Jacobians and the Sato Grassmannian

摘要

In this paper, a one-dimensional family of stratifications on a hypereUiptic Jacobian is introduced. It generalizes a well-known stratification, considered in algebraic geometry, in the contract 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.