On the parameter space of B\"or\"oczky configurations

TL;DR

This paper explores the parameter spaces of B"or"oczky line configurations, analyzing their structure and rational points to understand their role in the containment problem between symbolic and ordinary powers of ideals.

Contribution

It provides explicit descriptions of parameter families for B"or"oczky configurations with 13, 14, 16, 18, and 24 lines, and studies their rational points.

Findings

Parameter families for specific B"or"oczky configurations are described.

Rational points in these parameter spaces are investigated.

Connections to the containment problem in algebraic geometry are discussed.

Abstract

B\"or\"oczky 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 B\"or\"oczky configurations of 13, 14, 16, 18 and 24 lines and investigate rational points of these parameter spaces.