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<p>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.</p>

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On the Coordinate Rings of Calogero-Moser Spaces and the Invariant Commuting Variety of a Pair of Matrices

  • 期刊论文

  • 发表日期：

    2025年3月12日

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  • Farkhod Eshmatov,
  • Xabier García-Martínez,
  • Zafar Normatov,
  • Rustam Turdibaev

摘要

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.