Quiver schemes for non-generic stability and cornering

Abstract

We use the Le Bruyn–Procesi theorem to prove several results on quiver schemes for non-generic stability conditions: We show that the stability-zero finite ADE-type Nakajima quiver schemes are reduced points and give an example of a closely related non-reduced quiver scheme. In broader generality, we prove that adding modules supported on stability-zero vertices induces closed embeddings of quiver schemes, and show how in many cases the quiver scheme associated with the cornered algebra defines a limit to this system of embeddings. As an application, we show that there is an isomorphism between the underlying reduced schemes of certain equivariant Quot schemes and Nakajima quiver varieties.