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Open AccessArticle

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
Mathematics 2014, 2(4), 218-231; https://doi.org/10.3390/math2040218
Received: 19 June 2014 / Revised: 9 October 2014 / Accepted: 13 October 2014 / Published: 16 October 2014
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
MDPI and ACS Style

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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