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arXiv · 2307.06098

On the coordinate rings of Calogero-Moser spaces and the invariant commuting variety of a pair of matrices

Farkhod Eshmatov·Xabier García-Martínez·Zafar Normatov·Rustam Turdibaev
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Abstract

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.

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Farkhod Eshmatov, Xabier García-Martínez, Zafar Normatov, Rustam Turdibaev. 2023-07-12. On the coordinate rings of Calogero-Moser spaces and the invariant commuting variety of a pair of matrices. https://arxiv.org/abs/2307.06098

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