On the containment $I^{(3)}\subseteq I^2$ and configurations of triple points in Böröczky line arrangements

Abstract

We study sets of triple points of Böröczky's arrangements of lines in the context of the containment problem proposed by Harbourne and Huneke. We show that in the class of those arrangements, the smallest counterexample to the containment $I^{(3)}\subseteq I^2$ is obtained when the number of lines is equal to 12.