On the coordinate rings of Calogero-Moser spaces and the invariant commuting variety of a pair of matrices
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909502504173568 |
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| author | Eshmatov, Farkhod García-Martínez, Xabier Normatov, Zafar Turdibaev, Rustam |
| author_facet | Eshmatov, Farkhod García-Martínez, Xabier Normatov, Zafar Turdibaev, Rustam |
| contents | This paper presents a comprehensive description of the coordinate rings and Poisson brackets associated with the fourth Calogero-Moser space and invariant commuting pairs of matrices of size four. As an application, we compute their respective classes in the Grothendieck ring of the category of complex varieties and we offer some novel insights about the geometry of the Hilbert scheme of points on the affine plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_06098 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the coordinate rings of Calogero-Moser spaces and the invariant commuting variety of a pair of matrices Eshmatov, Farkhod García-Martínez, Xabier Normatov, Zafar Turdibaev, Rustam Algebraic Geometry Rings and Algebras Representation Theory 16R30, 13A50, 14R20, 14L30, 17B63 This paper presents a comprehensive description of the coordinate rings and Poisson brackets associated with the fourth Calogero-Moser space and invariant commuting pairs of matrices of size four. As an application, we compute their respective classes in the Grothendieck ring of the category of complex varieties and we offer some novel insights about the geometry of the Hilbert scheme of points on the affine plane. |
| title | On the coordinate rings of Calogero-Moser spaces and the invariant commuting variety of a pair of matrices |
| topic | Algebraic Geometry Rings and Algebras Representation Theory 16R30, 13A50, 14R20, 14L30, 17B63 |
| url | https://arxiv.org/abs/2307.06098 |