Freeness and near freeness are combinatorial for line arrangements in small degrees
arXiv:1712.04400
Abstract
We prove Terao conjecture saying that the freeness is determined by the combinatorics for arrangements of 13 lines in the complex projective plane and that the property of being nearly free is combinatorial for line arrangements of up to 12 lines in the complex projective plane.
v2: improved presentation, new section added (section 4, main results Thm 4.9, Prop. 4.10)