Nested Hilbert Schemes on Hirzebruch surfaces and quiver varieties
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911166794563584 |
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| author | Bruzzo, Ugo Lanza, Valeriano Santos, Pedro H. Dos |
| author_facet | Bruzzo, Ugo Lanza, Valeriano Santos, Pedro H. Dos |
| contents | For $n\ge 1$ we show that the length 1 nested Hilbert scheme of the total space $X_n$ of the line bundle $\mathcal O_{\mathbb P^1}(-n)$, parameterizing pairs of nested 0-cycles in $X_n$, is a quiver variety associated with a suitable quiver with relations. This generalizes previous work about nested Hilbert schemes on $\mathbb C^2$ in one direction, and about the Hilbert schemes of points of $X_n$ in another direction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18099 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nested Hilbert Schemes on Hirzebruch surfaces and quiver varieties Bruzzo, Ugo Lanza, Valeriano Santos, Pedro H. Dos Algebraic Geometry Representation Theory 14C05, 14D20, 14D23, 14J10, 14J26, 16G20 For $n\ge 1$ we show that the length 1 nested Hilbert scheme of the total space $X_n$ of the line bundle $\mathcal O_{\mathbb P^1}(-n)$, parameterizing pairs of nested 0-cycles in $X_n$, is a quiver variety associated with a suitable quiver with relations. This generalizes previous work about nested Hilbert schemes on $\mathbb C^2$ in one direction, and about the Hilbert schemes of points of $X_n$ in another direction. |
| title | Nested Hilbert Schemes on Hirzebruch surfaces and quiver varieties |
| topic | Algebraic Geometry Representation Theory 14C05, 14D20, 14D23, 14J10, 14J26, 16G20 |
| url | https://arxiv.org/abs/2403.18099 |