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