We classify the periodic Hamiltonian flows on com-
pact four dimensional symplectic manifolds up to isomorphism of
Hamiltonian Sx-spaces. Additionally, we show that all these spaces
are Kahler, that every such space is obtained 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.
1991 Mathematics Subject Classification. Primary 58F05, 70H33; Secondary