so（4）x so（4）上的Lagrange双凸与Prym簇的几何
The Lagrange bitop on so(4) x so(4) and geometry of the Prym varieties
摘要：
考虑了一个四维可积刚体系统，证明了它表示两个扭曲的三维Lagrange顶。本文提出了一种多项式Lax表示，它既不符合Dubrovin图象，也不符合Adler-van Moerbeke图象.代数几何积分过程是基于超椭圆曲线的双重覆盖的Prym变量的几何学的深层事实。所有这样的覆盖与Prym品种分裂为两个品种的总和相同的尺寸和可积的层次与初始系统之间的对应关系的建立。
英文摘要：
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 varietiesof double coverings of hypeelliptic curves. 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.
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