Quiver Schemes for Nongeneric Stability and Cornering

Fuente: arXiv
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Main Authors: Bertsch, Lukas, Gammelgaard, Søren
Format: Preprint
Published: 2025
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_version_ 1866915332889772032
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
id 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