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

Alexander Varchenko
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Alexander Varchenko: Department of Mathematics, University of North Carolina at Chapel Hill Chapel Hill, NC 27599-3250, USA

Mathematics, 2014, vol. 2, issue 4, 1-14

Abstract: 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.

Keywords: Master function; Lagrangian variety; Characteristic variety; Bethe ansatz (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2014
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