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arXiv · 2107.01945

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

Zafar Normatov·Rustam Turdibaev
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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 $3\times3$ invariant matrices involving the defining relations of $\mathbb{C}[\mathcal{C}_3]$. We find an explicit description of the commuting variety of $3\times3$ matrices and its orbits under the action of the affine Cremona group.

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Zafar Normatov, Rustam Turdibaev. 2021-07-05. Calogero-Moser spaces and the invariants of two matrices of degree 3. https://doi.org/10.1007/s00031-022-09776-y

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