On the containment problem and sporadic simplicial line arrangements

TL;DR

This paper presents two unique examples of sporadic simplicial arrangements of 31 lines that are inductively free, providing a negative answer to a recent containment problem posed by Drabkin and Seceleanu.

Contribution

It introduces two new non-isomorphic sporadic simplicial arrangements of lines that challenge existing assumptions in the containment problem.

Findings

Two non-isomorphic sporadic simplicial arrangements of 31 lines are inductively free.

These arrangements provide a negative answer to the containment problem.

The results expand understanding of simplicial arrangements and their algebraic properties.

Abstract

In the paper we present two examples of inductively free sporadic simplicial arrangements of 31 lines that are non-isomorphic, which allow us to answer negatively questions on the containment problem recently formulated by Drabkin and Seceleanu.