Symplectic toric orbifolds

Abstract

A symplectic toric orbifold is a compact connected orbifold $M$, a symplectic form $\omega$ on $M$, and an effective Hamiltonian action of a torus $T$ on $M$, where the dimension of $T$ is half the dimension of $M$. We prove that there is a one-to-one correspondence between symplectic toric orbifolds and convex rational simple polytopes with positive integers attached to each facet.

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Cited by in corpus (6)

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• Geodesic flows and contact toric manifolds
• Contact toric manifolds
• Toric integrable geodesic flows
• Toric symplectic singular spaces I: isolated singularities