Cohomologies of Affine Hyperelliptic Jacobi Varieties and Integrable Systems
Cohomologies of Affine Hyperelliptic Jacobi Varieties and Integrable Systems
复制标题
仿射超椭圆雅可比簇的上同调与可积系统
DOI：
10.1007/s002200100382
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发表时间：
2000
影响因子：
2.4
通讯作者：
F. Smirnov
中科院分区：
文献类型：
--
作者：
A. Nakayashiki;F. Smirnov
我们研究超椭圆曲线的仿射雅可比簇的仿射环。 Mumford 的仿射超椭圆雅可比簇的矩阵构造被用来计算仿射环的特征。通过分解该特征，我们对仿射超椭圆雅可比簇的上同调群做出了一些猜想。在这些仿射超椭圆雅可比簇描述的可积系统中，仿射环与相空间上的函数代数、经典可观测量密切相关。我们证明仿射环是由最高上同调群在不变向量场对雅可比簇的作用下生成的。
We study the affine ring of the affine Jacobi variety of a hyperelliptic curve. The matrix construction of the affine hyperelliptic Jacobi varieties due to Mumford is used to calculate the character of the affine ring. By decomposing the character we make several conjectures on the cohomology groups of the affine hyperelliptic Jacobi varieties. In the integrable system described by the familly of these affine hyperelliptic Jacobi varieties, the affine ring is closely related to the algebra of functions on the phase space, classical observables. We show that the affine ring is generated by the highest cohomology group over the action of the invariant vector fields on the Jacobi variety.