Free multiderivations of connected subgraph arrangements

TL;DR

This paper extends the classification of free arrangements from connected subgraph arrangements to their multiarrangement counterparts, identifying all graphs supporting a multiplicity that makes the arrangement free.

Contribution

It generalizes previous results by classifying graphs for which associated multiarrangements are free, broadening understanding of free multiarrangements.

Findings

Extended classification to multiarrangements

Identified all graphs supporting free multiarrangements

Generalized previous free arrangement results

Abstract

Cuntz and K\"uhne introduced the class of connected subgraph arrangements $A_G$, depending on a graph $G$, and classified all graphs $G$ such that the corresponding arrangement $A_G$ is free. We extend their result to the multiarrangement case and classify all graphs $G$ for which the corresponding arrangement $A_G$ supports some multiplicity $\mu$ such that the multiarrangement $(A_G,\mu)$ is free.