Abstract
We study the asymptotic form of the Gopakumar–Vafa invariants at all genera for Calabi–Yau toric threefolds which have the structure of fibration of the A n singularity over P 1. We claim that the asymptotic form is the inverse Laplace transform of the corresponding instanton amplitude in the prepotential of N=2 SU( n+1) gauge theory coupled to external graviphoton fields, which is given by the logarithm of the Nekrasov's partition function.
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