The symplectic holomorphic density property for Calogero-Moser spaces

TL;DR

This paper introduces new density properties for Calogero-Moser spaces, extending Andersén-Lempert theory, and characterizes their holomorphic symplectic automorphism groups.

Contribution

It establishes the symplectic and Hamiltonian holomorphic density properties for Calogero-Moser spaces, a novel extension of existing complex geometric theories.

Findings

Calogero-Moser space $\\mathcal{C}_n$ satisfies the introduced density properties.

The group of holomorphic symplectic automorphisms of $\mathcal{C}_n$ is described.

New versions of Andersén-Lempert theory are developed for these spaces.

Abstract

We introduce the symplectic holomorphic density property and the Hamiltonian holomorphic density property together with the corresponding version of Anders\'en-Lempert theory. We establish these properties for the Calogero-Moser space $\mathcal{C}_n$ of $n$ particles and describe its group of holomorphic symplectic automorphisms.