5 problems

Let $\mathcal{A}$ be a unimodular arrangement, let $\mathfrak{M}(\mathcal{A})$ be the associated hypertoric variety, and let $R(\mathcal{A})$ be the ring generated by the elements…

Gammage–McBreen–Webster conjecture. There exists an additive variety $\mathfrak{M}$, a divisor $\mathfrak{D} \in \mathfrak{M}$, and an isomorphism

The hypertoric intersection-cohomology conjecture. For all $n$, there exists an isomorphism of graded $\mathfrak{S}_n$-representations

Additive realization conjecture. Every multiplicative hypertoric variety admits an additive realization: there exists an additive hypertoric variety $\mathfrak{M}$, a divisor…

Let $K$ be a subtorus of a torus $T$, let $\boldsymbol{\chi}=(\chi_i)$ be the associated characters, and let $\alpha$ be as in the construction of the hypertoric variety. For each…