A Computational Criterion for the Supersolvability of Line Arrangements

Abstract

In this note we find a necessary and sufficient condition for the supersolvability of an essential, central arrangement of rank \(3\) (\(i.e\), line arrangement in the projective plane). We present an algorithmic way to decide if such an arrangement is supersoivable or not that does not require an ordering of the lines as the Bjémer-Ziegler’s and Peeva’s criteria require. The method uses the duality between points and lines in the projective plane in the context of coding theory.