On the freeness of B\xf6r\xf6czky line arrangements

Abstract

In the present note, we focus on the freeness and some combinatorial properties of line arrangements in the projective plane having only double and triple points. The main result shows that for this class of line arrangements the freeness property is combinatorially determined. As a corollary, we show that Böröczky line arrangements in the sense of Füredi and Palásti (Proc Am Math Soc 92(4):561–566, 1984), except exactly three cases, are not free.