Gammage–McBreen–Webster conjecture on multiplicative hypertoric varieties

Let $\mathfrak{U}$ be a multiplicative hypertoric variety.

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

$$\mathfrak{U} \simeq \mathfrak{M} \setminus \mathfrak{D}.$$

This conjecture proposes a relation between multiplicative and additive hypertoric varieties, in the spirit of mirror symmetry for Hitchin systems. The source presents the proposal as highly speculative and based on formal similarities rather than concrete evidence.