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arXiv 1402.0924math.AGmath.CO
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一般平移排列的Gauss-Manin微分方程的特征簇

Characteristic variety of the Gauss-Manin differential equations of a generic parallelly translated arrangement

Alexander Varchenko

摘要:

我们考虑$\C^k$中的一类加权的$n$广义平移超平面,并描述了相应超几何积分的Gauss-Manin微分方程的特征多样性.特征簇是Laurent多项式的零集,其系数由Grassmannian Gr(k,n)中相应点的Plucker坐标和权决定.罗朗多项式是对合的。

英文摘要:

We consider a weighted family of $n$ generic parallelly translated hyperplanes in $\C^k$ and describe the characteristic variety of the Gauss-Manin differential equations for associated hypergeometric integrals. The characteristic variety is given as the zero set of Laurent polynomials, whose coefficients are determined by weights and the Plucker coordinates of the associated point in the Grassmannian Gr(k,n). The Laurent polynomials are in involution.

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