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Mathematics 2014, 2(4), 218-231; doi:10.3390/math2040218

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

Department of Mathematics, University of North Carolina at Chapel Hill Chapel Hill, NC 27599-3250, USA
Received: 19 June 2014 / Revised: 9 October 2014 / Accepted: 13 October 2014 / Published: 16 October 2014
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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. View Full-Text
Keywords: Master function; Lagrangian variety; Characteristic variety; Bethe ansatz Master function; Lagrangian variety; Characteristic variety; Bethe ansatz
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Varchenko, A. Characteristic Variety of the Gauss–Manin Differential Equations of a Generic Parallelly Translated Arrangement. Mathematics 2014, 2, 218-231.

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