4 problems

Existence conjecture for curves of type $(d,r,m)$. For any integers $d,m\geq 3$ and any integer $r$ such that

Let $\mathcal A:f=0$ be a line arrangement of degree $d$ in the complex projective plane. Let $\operatorname{mdr}(f)$ denote the minimal degree of a Jacobian relation for $f$, and…

Let ${\mathcal A}$ and ${\mathcal B}$ be arrangements of $d$ lines with isomorphic intersection lattices … Let $r({\mathcal A})$ denote the minimal degree of a Jacobian relation. S…

Let ${\mathcal A}$ and ${\mathcal B}$ be line arrangements with isomorphic intersection lattices … For an arrangement ${\mathcal A}$, let $r({\mathcal A})$ denote the minimal degre…