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

Author:

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

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Rings and Algebras (math.RA), Representation Theory (math.RT)

journal:

date:

2023-07-11 16:00:00

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 offer some novel insights into the geometry of the Hilbert scheme of points on the affine plane.

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