Rational singularities for codimension-one orbit closures of arbitrary quivers

Let $Q$ be a quiver. For an extended Dynkin quiver, let $T_1,\dots,T_m$ be pairwise non-isomorphic indecomposables in $\operatorname{Rep}(Q)$ such that $\operatorname{Ext}(T_i,T_j)=0$ for all $i,j\leq m$. There is a positive integer $N$ such that all codimension-$1$ orbit closures in $\operatorname{Rep}(Q,\alpha)$ have rational singularities for every dimension vector

$$\alpha=\lambda_1\cdot\underline{d}(T_1)+\dots+\lambda_m\cdot\underline{d}(T_m),$$

with $\lambda_i\geq N$ for $i=1,\dots,m$. General quiver conjecture. The same assertion is true for any quiver $Q$. The preceding theorem establishes this assertion for extended Dynkin quivers; the conjecture extends the expected rational-singularity property to arbitrary quivers.