On the parameter spaces of some Böröczky configurations

Abstract

Böröczky configurations of lines have been recently considered in connection with the problem of the containment between symbolic and ordinary powers of ideals. Here, we describe parameter families of Böröczky configurations of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] lines and investigate rational points of these parameter spaces.