dedicated to henry crapo on his 65th birthday
Let G(r, 1, l ) be the complex arrangement
where ! is a primitive rth root of unity. The matroids of these arrangements are the Dowling matroids Q l (Z r ), where Z r is the group of rth roots of unity. We show that if E is a subset of G(r, 1, l ) which does not contain any matroid line, then deleting E gives an arrangement G(r, 1, l )"E which is free. We also give necessary and sufficient conditions on a set E containing at least one matroid line but no matroid planes so that the deletion G(r, 1, l )"E has a characteristic polynomial which factors completely over the integers. Two types of arrangements can be obtained in this way. We show that one type is always non-free. This yields examples of non-free complex arrangements whose characteristic polynomials factor completely over the integers. The same ideas also yield examples of non-free arrangements over any sufficiently large field (and hence, over the reals) with characteristic polynomials which factor completely over the integers. The matroids of these arrangements are non-supersolvable matroids whose characteristic polynomials factor completely over the integers.