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In the first part of the paper, we build a foundation for further work onHamiltonian actions on symplectic orbifolds. Most importantly we prove theorbifold versions of the abelian connectedness and convexity theorems.  In the second half, we prove that compact symplectic orbifolds withcompletely integrable torus actions are classified by convex simple rationalpolytopes with a positive integer attached to each facet and that all suchorbifolds are algebraic toric varieties.

Hamiltonian torus actions on symplectic orbifolds and toric varieties