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From compact semi-toric systems to Hamiltonian $S^1$-spaces

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  • We show how any labeled convex polygon associated to a compact semi-toric system, as defined by Vũ ngọc, determines Karshon's labeled directed graph which classifies the underlying Hamiltonian $S^1$-space up to isomorphism. Then we characterize adaptable compact semi-toric systems, i.e. those whose underlying Hamiltonian $S^1$-action can be extended to an effective Hamiltonian $\mathbb{T}^2$-action, as those which have at least one associated convex polygon which satisfies the Delzant condition.
    Mathematics Subject Classification: Primary: 37J05, 37J35, 53D20.

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