F.-N.'s deformation conjecture for symplectic resolutions

Let $Z$ be a normal symplectic singularity, and let $f_i:X_i\to Z$, $i=1,2$, be symplectic resolutions. A flat deformation is a flat family over a parameter space $T$ with central fibre the given resolution or singularity.

F.-N.'s conjecture. There are flat deformations

$$\mathcal{X}_i\stackrel{F_i}\to\mathcal{Z}\to T$$

of the resolutions such that, for $t\in T-\{0\}$, the maps $F_{i,t}:\mathcal{X}_{i,t}\to\mathcal{Z}_t$ are isomorphisms.

This is a formulation of the deformation-equivalence expectation for symplectic resolutions. The paper applies the corresponding idea to nilpotent orbit closures in classical Lie algebras, while the general conjecture is not resolved in the source.