Terao's conjecture asserts that two central hyperplane arrangements over the same field with isomorphic intersection lattices are either both free arrangements or both nonfree (Anghel and Stan 2026). Thus the question is whether freeness is a combinatorial property, rather than a property of a particular geometric realization.
Anghel and Stan (2026) proved the conjecture for arrangements of 15 and 16 lines in the complex projective plane. Together with
earlier results, this establishes it for every central arrangement of at most 16
planes in 
. It does not settle the conjecture for arbitrary
numbers of hyperplanes, arbitrary dimensions, or arbitrary
fields.
In a different dimension, Jarosławski (2026) proved the conjecture for arrangements of at most nine planes in complex projective space 
. These correspond to central hyperplane arrangements
in 
, rather than to the arrangements in 
above.
