Triangular arrangements on the projective plane

In this work we study line arrangements consisting in lines passing through three non-aligned points. We call them triangular arrangements. We prove that any combinatorics of a triangular arrangement is always realized by a Roots-of-Unity-Arrangement, which is a particular class of triangular arrangements. Among these Roots-of Unity-Arrangements, we provide conditions that ensure their freeness. Finally, we give two triangular arrangements having the same weak combinatorics, such that one is free but the other one is not.
Comment: 20 pages. Published in \'Epijournal de G\'eom\'etrie Alg\'ebrique. Section 4 has been deeply revised due to an incorrect statement pointed out by the referee