8 problems

Let a $(4,d)$-multinet be a multinet on a hyperplane arrangement with four classes and weight $d$, and call it non-trivial when it is not the trivial multinet. Yuzvinsky's conjectu…

A multinet in $\mathbb{CP}^2$ is a line arrangement with the multinet structure defined in the paper, and a net is the corresponding structure with all line multiplicities equal to…

A pencil of plane curves is said to be of rank three when it has three completely reducible fibers satisfying the other condition of Definition. Connectedness conjecture for rank-t…

A $4$-net is a line arrangement equipped with a partition into four classes satisfying the net incidence conditions. The Hessian arrangement is the known example of a $4$-net. Hess…

Let $L$ be a line arrangement in ${\mathbb P}^2$, let $F_f$ be the Milnor fiber of a defining polynomial $f$, and let $H^1(F_f,{\mathbb C})_\lambda$ denote the $\lambda$-eigenspace…

Yuzvinsky's uniqueness conjecture. The Hesse configuration is the unique 4-net up to projective isomorphism.

The Hasse configuration is the $(4,3)$-net arising from the completely reducible fibers $xyz$ and $x^3+y^3+z^3$ of a Ceva pencil. Hasse configuration uniqueness conjecture. The Has…

Let $c\mathcal{A}$ be the cone over a real line arrangement $\mathcal{A}$, and suppose that $c\mathcal{A}$ is a simplicial arrangement. Let $F_{\mathcal{A}}$ denote the Milnor fibe…