The symplectic-resolution deformation-equivalence conjecture

Let $X$ be an irreducible variety with symplectic singularities, and suppose that there are two projective symplectic resolutions

$$Z_1\rightarrow X,\qquad Z_2\rightarrow X.$$

Symplectic-resolution deformation-equivalence conjecture. Then $Z_1$ is deformation equivalent to $Z_2$.

This conjecture proposes that the deformation type of a projective symplectic resolution depends only on the underlying symplectic singularity. The paper proves the assertion for nilpotent orbit closures in simple complex Lie algebras of classical type; the general case remains open.