Journal of Differential Geometry

Mirror symmetry for orbifold Hurwitz numbers

Vincent Bouchard, Daniel Hernández Serrano, Xiaojun Liu, and Motohico Mulase

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We study mirror symmetry for orbifold Hurwitz numbers. We show that the Laplace transform of orbifold Hurwitz numbers satisfy a differential recursion, which is then proved to be equivalent to the integral recursion of Eynard and Orantin with spectral curve given by the $r$-Lambert curve. We argue that the $r$-Lambert curve also arises in the infinite framing limit of orbifold Gromov-Witten theory of $[\mathbb{C}^3 / (\mathbb{Z} / r\mathbb{Z})]$. Finally, we prove that the mirror model to orbifold Hurwitz numbers admits a quantum curve.

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J. Differential Geom., Volume 98, Number 3 (2014), 375-423.

First available in Project Euclid: 28 July 2014

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Bouchard, Vincent; Serrano, Daniel Hernández; Liu, Xiaojun; Mulase, Motohico. Mirror symmetry for orbifold Hurwitz numbers. J. Differential Geom. 98 (2014), no. 3, 375--423. doi:10.4310/jdg/1406552276.

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