Hamiltonian Gromov–Witten invariants on ℂ n+1 with S 1-action

Abstract

Consider a Hamiltonian action of S1 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 $$H_{{S^1},CR}^*\left( {X,R} \right)$$ 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.