# Lagrangian cores of quiver variety in different GIT chambers

Let $$\pi: \mathfrak{M}_{(\theta,0)}(Q,\text{v},\text{w}) \rightarrow \mathfrak{M}_{(0,0)}(Q,\text{v},\text{w})$$ be the projective morphism between Nakajima quiver varieties when complex moment parameter is equal to zero $$\zeta_\mathbb{C}=0.$$ We define the Lagrangian core to be $$\Lambda_{\theta}=\pi^{-1}(0).$$

Now, when one varies the GIT-chamber of stability parameter $$\theta$$ (for rep theorists) $$\leftrightarrow$$ real moment map parameter (for hyperkähler geometers), it is expected that the corresponding core change in principle. Does anyone have examples of such different cores?