Prym Varieties and Integrable Systems

Details Prym Varieties and Integrable Systems Prym Varieties and Integrable Systems

1992-03-20

arxiv.org/abs/alg-geom/9203002v2

Communications in Analysis and Geometry, Volume 5, (1997) 279--332

Mathematics

Algebraic Geometry

37 pages in AMS-LaTeX format. Article updated following the published version. Default page size is US Letter

Scientific paper

A new relation between Prym varieties of arbitrary morphisms of algebraic curves and integrable systems is discovered. The action of maximal commutative subalgebras of the formal loop algebra of GL(n) defined on certain infinite-dimensional Grassmannians is studied. It is proved that every finite-dimensional orbit of the action of traceless elements of these commutative Lie algebras is isomorphic to the Prym variety associated with a morphism of algebraic curves. Conversely, it is shown that every Prym variety can be realized as a finite-dimensional orbit of the action of traceless diagonal elements of the formal loop algebra, which defines the multicomponent KP system.

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