  It is known that there exist hyperplane arrangements with same underlying
matroid that admit non-homotopy equivalent complement manifolds. In this work
we show that, in any rank, complex central hyperplane arrangements with up to 7
hyperplanes and same underlying matroid are isotopic. In particular, the
diffeomorphism type of the complement manifold and the Milnor fiber and
fibration of these arrangements are combinatorially determined, i.e., they
depend uniquely on the underlying matroid. To do this, we associate to every
such matroid a topological space, that we call the reduced realization space;
its connectedness, showed by means of symbolic computation, implies the desired
result.
