Hyperpolygonal arrangements

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 Hₙ . In this note, we study these arrangements and investigate their properties systematically. Remarkably, the arrangements Hₙ 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 H₅ is the famous counterexample of Edelman and Reiner [17] of Orlik’s conjecture that the restriction of a free arrangement is again free.