6 problems

Let $\mathcal{A}$ be a complex hyperplane arrangement with arrangement group $G=G(\mathcal{A})$. Let $R_1(\mathcal{A})=\bigcup_i L_i$ be its resonance variety, and set…

Let $\mathcal{A}$ be a complex hyperplane arrangement with arrangement group $G=G(\mathcal{A})$. Write the resonance variety as $R_1(\mathcal{A})=\bigcup_i L_i$, where the $L_i$ ar…

Let a hyperplane arrangement be given, and let a $(4,d)$-multinet be a multinet with four classes and degree $d$. Yuzvinsky's uniqueness conjecture. The only $(4,d)$-multinet on a…

Let $\mathsf{M}$ be a simple matroid. For each sub-matroid $\mathsf{M}'\subset \mathsf{M}$, let $n_k(\mathsf{M}')$ be the number of $k$-multinets supported by $\mathsf{M}'$, and le…

Let $E$ be an exterior algebra and let $J\subset E$ be a pure ideal, meaning an ideal generated by products of linear forms. Suppose that $E/J$ satisfies property (): any two disti…

Let ${\mathcal{A}}$ be a hyperplane arrangement, let $G=G({\mathcal{A}})$ be its arrangement group, and let $R^{1}({\mathcal{A}})$ be its first resonance variety. For each $r$, let…