## Computing certain Gromov-Witten invariants of the crepant resolution of $$\mathbb{P}(1,3,4,4)$$.(English)Zbl 1230.53081

Summary: 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 $$\mathbb{P}(1,3,4,4)$$.

### MSC:

 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds 14J33 Mirror symmetry (algebro-geometric aspects) 14M25 Toric varieties, Newton polyhedra, Okounkov bodies 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)

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