8 problems

Supersolvable arrangement double-point conjecture. One has

Fixed-invariant finiteness conjecture. For fixed $\sigma(\mathcal{A})$, the set of non-supersolvable arrangements $\mathcal{A}$ is finite in characteristic zero.

Supersolvable Sylvester–Gallai conjecture. One has

Let $t_2$ denote the number of crossing points of multiplicity $2$ in a complex line arrangement, and let $s$ be the number of its lines. A non-pencil complex supersolvable line ar…

Let $t_2$ denote the number of crossing points of multiplicity $2$ in a complex line arrangement. An arrangement is nontrivial if it is neither a pencil nor a near pencil, and it i…

Tohăneanu's low-exponent supersolvability conjecture. Then $\mathcal{A}$ is supersolvable. The conjecture concerns free arrangements with exactly one exponent equal to $3$ and is v…

Let $f_1,\ldots,f_m\in\mathbb C[x,y]$ be linear forms such that $\gcd(f_i,f_j)=1$ for all $i\neq j$. For each pair $i<j$, let $\langle f_i+z,f_j+z\rangle$ denote the ideal of…

Let $\mathcal A\subset\mathbb P^2$ be a full-rank supersolvable arrangement of $n$ lines with a singular modular point $P$ of maximum multiplicity $m\geq 3$. A line has only triple…