Hyperpolygonal arrangements

Abstract In [5], a particular family of real hyperplane arrangements stemming from hyperpolygonal spaces associated with certain quiver varieties was introduced which we thus call hyperpolygonal arrangements ${\mathscr H}_n$ . In this note, we study these arrangements and investigate their properties systematically. Remarkably, the arrangements ${\mathscr H}_n$ discriminate between essentially all local properties of arrangements. In addition, we show that hyperpolygonal arrangements are projectively unique and combinatorially formal. We note that the arrangement ${\mathscr H}_5$ is the famous counterexample of Edelman and Reiner [17] of Orlik’s conjecture that the restriction of a free arrangement is again free.