On the freeness of Böröczky line arrangements (Q2416497)

In the projective plane the author considers arrangements of lines which have only double and triple points as the intersections. The freeness of line arrangements is defined via the freeness of modules. In the paper free line arrangements having only double and triple points are characterized. And namely, the main result states: if such a line arrangement is free, then the number of lines $\vert A\vert $ obeys the inequality $3 \le \vert A\vert \le 9$. \par This result is applied to Böröczky arrangements of lines in the sense of \textit{Z. Füredi} and \textit{I. Palásti} [Proc. Am. Math. Soc. 92, 561--566 (1984; Zbl 0521.51003)]. As a corollary, it is shown that the Böröczky line arrangements, with exception of exactly three cases, are not free.