3 problems

Points-and-lines conjecture. The underlying matroid of a free or $K(\pi,1)$ arrangement is determined by its points and lines.

Let ${\mathcal{A}}$ and ${\mathcal{A}}'$ be central arrangements in $\mathbb{C}^3$. Write $U({\mathcal{A}})$ for the complement, ${\partial{{\overline{U}}}}({\mathcal{A}})$ for its…

Let ${\mathcal{A}}$ be a central arrangement in $\mathbb{C}^3$, let $U({\mathcal{A}})$ be its complement, and let $L({\mathcal{A}})$ be its intersection lattice. Jiang–Yau's conjec…