Combinatorial symmetry of line arrangements and applications

It is clear that a geometric symmetry of a line arrangement induces a combinatorial one; we study the converse situation. We introduce a strategy that exploits a combinatorial symmetry in order to produce a geometric reflection. We apply this method to disqualify three real examples found in previous work by the authors from being Zariski pairs. Robustness is shown by its application to complex cases, as well, including the MacLane and Nazir–Yoshinaga arrangements.