Authors: Dragović, Vladimir 
Gajić, Borislav 
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
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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