Algebraic Geometry of the eigenvector mapping for a free rigid body
Algebraic Geometry of the eigenvector mapping for a free rigid body
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自由刚体特征向量映射的代数几何
DOI：
10.1016/j.difgeo.2011.04.023
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发表时间：
2011
影响因子：
0.5
通讯作者：
D.Tarama
中科院分区：
文献类型：
--
作者：
I.Naruki;D.Tarama
本文讨论自由刚体特征向量映射的代数几何问题。特征向量映射被认为是从椭圆曲线的乘积到复射影平面的有理映射，其中一条椭圆曲线是积分曲线，另一条是谱曲线。这是确定特征向量的必要数据的空间。特征向量映射允许通过库默表面，这是一个双重覆盖的投影平面分支沿着与动态相关联的六次曲线的因式分解。论证的关键是射影平面的Cremona变换和库默曲面的某些椭圆纤维化。
The present paper deals with the algebro-geometric aspects of the eigenvector mapping for a free rigid body. The eigenvector mapping is regarded as a rational mapping to the complex projective plane from the product of the elliptic curves, one of which is the integral curve and the other the spectral curve. This is the space of the necessary data to determine the eigenvectors. The eigenvector mapping admits a factorisation through a Kummer surface, which is a double covering of the projective plane branched along a sextic curve associated with the dynamics. The key of the argument is the Cremona transformation of the projective plane and some elliptic fibrations of the Kummer surface.