Smooth toric varieties come naturally with the structure of an integrable system by considering the moment map of the torus action. In the case of lower dimensional torus actions the situation is more complicated. Here, a recent result by Hohloch, Sabatini, Symington and Sepe gives an exact criterion for the existence of so-called semi-toric systems on an algebraic surface with C*-action. We compare symplectic and algebraic results for such surfaces and conclude that the existence of semi-toric systems on C*-surfaces is equivalent to the existence of an equivariant degeneration to a normal toric variety. This is joint work with Christophe Wacheux. |

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