Periodic Hamiltonian flows on four-dimensional manifolds

Abstract

We classify the periodic Hamiltonian flows on compact four dimensional symplectic manifolds up to isomorphism of Hamiltonian S 1 -spaces. Additionally, we show that all these spaces are Khler, 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. YAEL KARSHON Appendix C. Computing a Khler cone 65 References 70 We assume that this flow is periodic, with period 2, i.e., that M generates a circle action on M. The function is called the moment map for this action. The triple (M, , ) is called a Hamiltonian S 1space, or a Hamiltonian circle action, or a periodic Hamiltonian flow.