On Orbifold Criteria for Symplectic Toric Quotients

Abstract

We introduce the notion of regular symplectomorphism and graded regular symplectomorphism between singular phase spaces. Our main concern is to exhibit examples of unitary torus representations whose symplectic quotients cannot be graded regularly symplectomorphic to the quotient of a symplectic representation of a finite group, while the corresponding GIT quotients are smooth. Additionally, we relate the question of simplicialness of a torus representation to Gaussian elimination.

References in corpus (1)

• On the existence of star products on quotient spaces of linear Hamiltonian torus actions

Cited by in corpus (9)

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• Constructing symplectomorphisms between symplectic torus quotients
• Symplectic quotients and representability: the circle action case
• Multigraded Hilbert series of invariants, covariants, and symplectic quotients for some rank $1$ Lie groups