Quiver Schemes for Nongeneric Stability and Cornering
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915332889772032 |
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| author | Bertsch, Lukas Gammelgaard, Søren |
| author_facet | Bertsch, Lukas Gammelgaard, Søren |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_12156 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quiver Schemes for Nongeneric Stability and Cornering Bertsch, Lukas Gammelgaard, Søren Algebraic Geometry Primary 14D20, Secondary 16G20, 14D23, 14J17 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. |
| title | Quiver Schemes for Nongeneric Stability and Cornering |
| topic | Algebraic Geometry Primary 14D20, Secondary 16G20, 14D23, 14J17 |
| url | https://arxiv.org/abs/2505.12156 |