6 problems

Let $S=\mathbb C[x,y,z]$, let $\mathcal A:f=0$ be a line arrangement in $\mathbb P^2$, and write $d=\deg f$. Its minimal degree of a Jacobian relation is … where…

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 $C:f=0$ be a reduced plane curve of degree $d$, let $r$ be the minimal degree of a nonzero Jacobian syzygy, and let $m$ be the number of minimal generators of its Jacobian syzy…

Free-or-nearly-free conjecture. A reduced plane curve $C:f=0$ which is rational cuspidal is either free or nearly free.