Quiver Schemes for Nongeneric Stability and Cornering

Lukas Bertsch; Søren Gammelgaard

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arXiv · 2505.12156

Quiver Schemes for Nongeneric Stability and Cornering

Lukas Bertsch·Søren Gammelgaard

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Abstract

We use the Le Bruyn--Procesi theorem to prove several results on quiver schemes for nongeneric stability conditions: We show that the stability-zero finite-type Nakajima quiver schemes are reduced points and give an example of a closely related nonreduced 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.

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BibTeX RIS

Lukas Bertsch, Søren Gammelgaard. 2025-05-17. Quiver Schemes for Nongeneric Stability and Cornering. https://arxiv.org/abs/2505.12156

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