Heavy hyperplanes in multiarrangements and their freeness

TL;DR

This paper extends the class of known free arrangements by introducing unbalanced multiarrangements and generalizing freeness criteria, including Yoshinaga's, to higher dimensions and flags.

Contribution

It generalizes the concept of unbalanced arrangements to multiarrangements and extends freeness criteria to arbitrary dimensions using flags.

Findings

Generalization of unbalanced arrangements to multiarrangements

Extension of freeness criteria to higher dimensions

Broader class of arrangements where Terao's conjecture applies

Abstract

Only few categories of free arrangements are known in which Terao's conjecture holds. One of such categories consists of $3$-arrangements with unbalanced Ziegler restrictions. In this paper, we generalize this result to arbitrary dimensional arrangements in terms of flags by introducing unbalanced multiarrangements. For that purpose, we generalize several freeness criterions for simple arrangements, including Yoshinaga's freeness criterion, to unbalanced multiarrangements.