  We consider a weighted family of $n$ parallelly transported hyperplanes in a
$k$-dimensioinal affine space 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 associated point in the
Grassmannian Gr$(k,n)$. The Laurent polynomials are in involution.
  An intermediate object between the differential equations and the
characteristic variety is the algebra of functions on the critical set of the
associated master function. We construct a linear isomorphism between the
vector space of the Gauss-Manin differential equations and the algebra of
functions. The isomorphism allows us to describe the characteristic variety. It
also allowed us to define an integral structure on the vector space of the
algebra and the associated (combinatorial) connection on the family of such
algebras.
