Periodic Hamiltonian flows on four dimensional manifolds

We classify the periodic Hamiltonian flows on compact four dimensional symp lectic manifolds up to isomorphism of Hamiltonian S-1-spaces. Additionally, we show that all these spaces are Kahler, that every such space is obtaine d from a simple model by a Sequence of symplectic blowups, and that if the fixed points are isolated then the space is a toric variety.