  This article computes the Varchenko determinant of dehyperplane arrangements
which are generalizations of pseudohyperplane arrangements. But unlike those
latter, they are defined on a real manifold, and it is not always possible to
obtain a central dehyperplane arrangement by coning. This article also studies
the solution space of a linear system defined from a dehyperplane arrangement.
That equation system was first introduced by Aguiar and Mahajan for central
hyperplane arrangements.
