On the construction of certain 6-dimensional symplectic manifolds with Hamiltonian circle actions

Let be a connected, compact 6-dimensional symplectic manifold equipped with a semi-free Hamiltonian action such that the fixed point set consists of isolated points or surfaces. Assume dim . In an earlier paper, we defined a certain invariant of such spaces which consists of fixed point data and twist type, and we divided the possible values of these invariants into six ``types'. In this paper, we construct such manifolds with these ``types'. As a consequence, we have a precise list of the values of these invariants.