|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||The Lagrange bitop on so(4) × so(4) and geometry of the Prym varieties||Journal:||American Journal of Mathematics||Volume:||126||Issue:||5||First page:||981||Last page:||1004||Issue Date:||1-Oct-2004||Rank:||M21a||ISSN:||0002-9327||DOI:||10.1353/ajm.2004.0035||Abstract:||
A four-dimensional integrable rigid-body system is considered and it is shown that it represents two twisted three-dimensional Lagrange tops. A polynomial Lax representation, which doesn't fit neither in Dubrovin's nor in Adler-van Moerbeke's picture is presented. The algebro-geometric integration procedure is based on deep facts from the geometry of the Prym varieties of double coverings of hyperelliptic curves: Mumford's relation and Mumford-Dalalyan theory. The correspondence between all such coverings with Prym varieties splitted as a sum of two varieties of the same dimension and the integrable hierarchy associated to the initial system is established.
|Publisher:||The Johns Hopkins University Press||Project:||Serbian Ministry of Science and Technology, Project No. 1643|
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