Calogero-Moser spaces and the invariants of two matrices of degree 3

Abstract

We find a minimal set of generators for the coordinate ring of Calogero-Moser space ${\mathcal{C}}_3$ and the algebraic relations among them explicitly. We give a new presentation for the algebra of $3\times 3$ invariant matrices involving the defining relations of $\mathbb{C}[{\mathcal{C}}_3]$. We find an explicit description of the commuting variety of $3\times 3$ matrices and its orbits under the action of the affine Cremona group.

References in corpus (1)

• Defining relations of invariants of two 3 \times 3 matrices