Calogero-Moser Spaces and the Invariants of Two Matrices of Degree 3

We find a minimal set of generators for the coordinate ring of Calogero-Moser space C-3 and the algebraic relations among them explicitly. We give a new presentation for the algebra of 3 x 3 invariant matrices involving the defining relations of C[C-3]. Furthermore, we find an explicit description of the GL(3)-invariant commuting variety of 3x3 matrices and its orbits under the action of the affine plane Cremona group.

Automated summary

This paper investigates the generators and algebraic relations of the coordinate ring of Calogero-Moser space C-3, and provides a new presentation for the algebra of 3 x 3 invariant matrices. Additionally, it presents an explicit description of the GL(3)-invariant commuting variety of 3x3 matrices and its orbits under the action of the affine plane Cremona group.