The modular-flat freeness conjecture for hyperplane arrangements

Let ${\mathcal A}$ be a hyperplane arrangement, let $X$ be a modular flat, and let ${\mathcal A}_X$ and $c{\mathcal A}_{{\overline{v}}}$ denote the localization at $X$ and the coned fiber arrangement, respectively. An arrangement is free when its module of logarithmic derivations is free.

Modular-flat freeness conjecture. If $X$ is a modular flat and both ${\mathcal A}_X$ and $c{\mathcal A}_{{\overline{v}}}$ are free arrangements, then ${\mathcal A}$ is a free arrangement.

This conjecture extends freeness results associated with modular decompositions and is motivated by the fact that supersolvable arrangements are inductively free. Its resolution status is not specified in the source.