  We consider a weighted family of $n$ generic parallelly translated
hyperplanes in $\C^k$ 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 Plucker coordinates of the
associated point in the Grassmannian Gr(k,n). The Laurent polynomials are in
involution.
