Free multiderivations of connected subgraph arrangements

Abstract

Cuntz and Kühne 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 $\hat{I}¼$ such that the multiarrangement $(A_G,\hat{I}¼)$ is free.

25 pages, 2 figures; v2 updated acknowledgments; v3 final version; to appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze