Computing certain Gromov-Witten invariants of the crepant resolution of P(1,3,4,4)

Abstract

We prove a formula computing the Gromov-Witten invariants of genus zero with three marked points of the resolution of the transversal $A_3$-singularity of the weighted projective space $\mathbb{P}(1,3,4,4)$ using the theory of deformations of surfaces with $A_n$-singularities. We use this result to check Ruan’s conjecture for the stack $\mathbb{P}(1,3,4,4)$.