Centering toric arrangements of maximal rank

The homotopy type of the complement manifold of a complexified toric arrangement has been investigated by d'Antonio and Delucchi in a paper that shows the minimality of such topological space.

In this work we associate to a given toric arrangement a matrix that represents the arrangement over the integers.

Then, we consider the family of toric arrangements for which this matrix has maximal rank.

Our goal is to prove, by means of basic linear algebra arguments, that the complement manifold of the toric arrangements that belong to this family is diffeomorphic to that of centered toric arrangements and thus it is a minimal topological space, too.