Singular-locus hyperplane conjecture for quantizations of symplectic resolutions

Let $X$ be a symplectic resolution of the affine variety $X_0$, let $\mathfrak{p}=H^2(X)$, and let $\mathcal{A}_\lambda$ be the algebra of global sections of the quantization specialized at $\lambda\in H^2_{DR}(X)$. A hyperplane $\ker\alpha$ is a root hyperplane if the generic fiber of the universal deformation over it is not affine. Singular-locus hyperplane conjecture. The singular locus is a finite union of hyperplanes, each parallel to $\ker\alpha$ for some root $\alpha$. The conjecture proposes a uniform hyperplane description of parameters at which the quantized algebra fails to have finite homological dimension; the source presents it as a generalization of the quiver-variety situation.