Mathematics (Oct 2014)

Characteristic Variety of the Gauss–Manin DifferentialEquations of a Generic Parallelly Translated Arrangement

  • Alexander Varchenko

DOI
https://doi.org/10.3390/math2040218
Journal volume & issue
Vol. 2, no. 4
pp. 218 – 231

Abstract

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We consider a weighted family of \(n\) generic parallelly translated hyperplanes in \(\mathbb{C}^k\) 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 Plücker coordinates of the associated point in the Grassmannian Gr\((k,n)\). The Laurent polynomials are in involution.

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