Seiberg-like duality for resolutions of determinantal varieties
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913258098655232 |
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| author | Priddis, Nathan Shoemaker, Mark Wen, Yaoxiong |
| author_facet | Priddis, Nathan Shoemaker, Mark Wen, Yaoxiong |
| contents | We study the genus-zero Gromov-Witten theory of two natural resolutions of determinantal varieties, termed the PAX and PAXY models. We realize each resolution as lying in a quiver bundle, and show that the respective quiver bundles are related by a quiver mutation. We prove that generating functions of genus-zero Gromov-Witten invariants for the two resolutions are related by a specific cluster change of variables. Along the way, we obtain a quantum Thom-Porteous formula for determinantal varieties and prove a Seiberg-like duality statement for certain quiver bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05240 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Seiberg-like duality for resolutions of determinantal varieties Priddis, Nathan Shoemaker, Mark Wen, Yaoxiong Algebraic Geometry 14N35, 14M12 We study the genus-zero Gromov-Witten theory of two natural resolutions of determinantal varieties, termed the PAX and PAXY models. We realize each resolution as lying in a quiver bundle, and show that the respective quiver bundles are related by a quiver mutation. We prove that generating functions of genus-zero Gromov-Witten invariants for the two resolutions are related by a specific cluster change of variables. Along the way, we obtain a quantum Thom-Porteous formula for determinantal varieties and prove a Seiberg-like duality statement for certain quiver bundles. |
| title | Seiberg-like duality for resolutions of determinantal varieties |
| topic | Algebraic Geometry 14N35, 14M12 |
| url | https://arxiv.org/abs/2403.05240 |