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Conjecturally, any two symplectic resolutions are related by sequences of Mukai flops. Consider different symplectic resolutions coming from Hamiltonian reductions with different stability conditions. For example, two Nakajima quiver varieties $\mathcal{M}_{\theta_1,\zeta}(v,w)$ and $\mathcal{M}_{\theta_2,\zeta}(v,w)$ (we fix the dimension vectors $(v,w)$, fix the parameter $\zeta$ i.e., the image of moment map) with different regular (not on a wall) stability conditions $\theta_1$ and $\theta_2$. I was wondering whether in this case the conjecture follows from GIT generality.

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Actually, Namikawa recently proved the conjecture you're referring to (at least for symplectic cones with a "good" $C^*$ action), by establishing that every such symplectic resolution is a Mori dream space. For quiver varieties, I think one doesn't need to use Namikawa's results and can just think directly about variation of GIT; this won't always give flops, but it should in the context of a symplectic reduction for a flat moment map.

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