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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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