Terao’s freeness conjecture for hyperplane arrangements

Establish whether the freeness of the module of derivations tangent to a hyperplane arrangement is determined solely by the underlying matroid.

Background

The paper introduces the module of derivations tangent to an arrangement as a central object in the study of hyperplane arrangements. It notes that Terao’s conjecture concerns whether freeness is combinatorially determined by the arrangement’s underlying matroid. Although the paper studies more general hypersurface arrangements and their likelihood correspondences, this conjecture is cited as a longstanding unresolved question motivating the broader context of arrangement theory.