Free Arrangement

A free arrangement is a central hyperplane arrangement whose module of logarithmic derivations is a free module. More explicitly, let be a field, its polynomial ring, and , where is a linear functional defining . The relevant module is

The arrangement is free iff is free as an -module (Anghel and Stan 2026).

Terao's conjecture asks whether freeness is determined by the intersection lattice among hyperplane arrangements over the same field.