2014/10/09 by Alexander Varchenko, Varchenko, Alexander
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1410.2438
openalex publication_date 2014/10/09 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
We consider a weighted family of n parallelly transported hyperplanes in a\nk-dimensioinal affine space and describe the characteristic variety of the\nGauss-Manin differential equations for associated hypergeometric integrals. The\ncharacteristic variety is given as the zero set of Laurent polynomials, whose\ncoefficients are determined by weights and the associated point in the\nGrassmannian Gr(k,n). The Laurent polynomials are in involution.\n An intermediate object between the differential equations and the\ncharacteristic variety is the algebra of functions on the critical set of the\nassociated master function. We construct a linear isomorphism between the\nvector space of the Gauss-Manin differential equations and the algebra of\nfunctions. The isomorphism allows us to describe the characteristic variety. It\nalso allowed us to define an integral structure on the vector space of the\nalgebra and the associated (combinatorial) connection on the family of such\nalgebras.\n