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.



Nakajima quiver varieties with different stability conditions related by sequence of Mukai-flops?
Actually, Namikawa recently [proved the conjecture](https://arxiv.org/abs/1305.1698) 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.


