Freeness of line arrangements with many concurrent lines (Q2906702)

Let \(D\) be the reduced divisor associated to a line arrangement in \(\mathbb P^2 =\mathbb P(\mathbb C[x_0,x_1,x_2])\). The main open question about these bundles (also valid on \(\mathbb P^n\), for \(n \geq 2\)) is the so-called Terao's conjecture: Freeness of \(D\) depends only on its combinatorial type (i.e. the intersection lattice associated to the arrangement).NEWLINENEWLINEThe authors propose a new approach to Terao's conjecture, based on projective duality: any line of the divisor \(D\) corresponds to a point in \(\mathbb P^{2\vee}\). In this way they associate to \(D\) a finite set \(Z\) of points in \(\mathbb P^{2\vee}\) and they prove that Terao's conjecture is true for a free divisor \(D_Z \subset\mathbb P^2\) of type \((n, n + r)\), with \(r \geq 0\), as soon as \((n + 2)\) points of \(Z\) are collinear.NEWLINENEWLINEFor the entire collection see [Zbl 1239.00060].