Hamiltonian Gromov–Witten Invariants on C~(n+1) with S~1-action

Consider a Hamiltonian action of S~1 on(C~(n+1), ω_(std)), we shown that the Hamiltonian Gromov–Witten invariants of it are well-defined. After computing the Hamiltonian Gromov–Witten invariants of it, we construct a ring homomorphism from H*_(S~1,CR)(X, R) to the small orbifold quantum cohomology of X //_τ S~1 and obtain a simpler formula of the Gromov–Witten invariants for weighted projective space.