Arrangements and Frobenius like structures
Arrangements and Frobenius like structures
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排列和类似弗罗贝尼乌斯的结构
DOI：
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发表时间：
2012
期刊：
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通讯作者：
A. Varchenko
中科院分区：
文献类型：
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作者：
A. Varchenko
我们考虑一族C^k$中$n$超平面的一般加权安排，并证明了相关超几何积分的Gauss-Manin连接，奇异向量空间上的逆变形式，以及主函数临界集上的函数代数在一族的基础上定义了一个Frobenius结构.作为这种构造的结果，我们证明了高斯-马宁联络的线性算子的矩阵元由一族基上的单个函数的2k+1阶导数给出，该函数称为第二类势，见公式（6.46）。
We consider a family of generic weighted arrangements of $n$ hyperplanes in $C^k$ and show that the Gauss-Manin connection for the associated hypergeometric integrals, the contravariant form on the space of singular vectors, and the algebra of functions on the critical set of the master function define a Frobenius like structure on the base of the family. As a result of this construction we show that the matrix elements of the linear operators of the Gauss-Manin connection are given by the 2k+1-st derivatives of a single function on the base of the family, the function called the potential of second kind, see formula (6.46).