Acyclic quiver representations degenerate to zero
= Acyclic quiver representations degenerate to zero
Choose integer vertex weights increasing along every arrow of a finite acyclic <quiver>. Acting at vertex $i$ by $t^{w_i}I$ multiplies each arrow by a positive power of $t$. At $t=0$ all arrows vanish. Thus every orbit closure contains the origin of the <quiver representation space>.