Triangular arrangements on the projective plane

Abstract

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.

20 pages. Published in Épijournal de Géométrie Algébrique. Section 4 has been deeply revised due to an incorrect statement pointed out by the referee

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