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Convexity of Singular Affine Structures and Toric-Focus Integrable Hamiltonian Systems J. Gates there have been more thanThis work is devoted to a systematic study of symplectic convexity for integrable Hamiltonian systems with elliptic and focus focus singularities. A distinctive feature of these systems is that their base spaces are still smooth manifolds (with boundary and corners), analogous to the toric case, but their associated integral affine structures are singular, with non trivial monodromy, due to focus singularities. We obtain a series of convexity results,