Abstract
We prove a formula computing the Gromov-Witten invariants of genus zero with three marked points of the resolution of the transversal A3 - singularity of the weighted projective space P(1, 3, 4, 4) using the theory of deformations of surfaces with An -singularities. We use this result to check Ruan's conjecture for the stack P(1, 3, 4, 4).