Open Access
November 2014 Mirror symmetry for orbifold Hurwitz numbers
Vincent Bouchard, Daniel Hernández Serrano, Xiaojun Liu, Motohico Mulase
J. Differential Geom. 98(3): 375-423 (November 2014). DOI: 10.4310/jdg/1406552276


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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Vincent Bouchard. Daniel Hernández Serrano. Xiaojun Liu. Motohico Mulase. "Mirror symmetry for orbifold Hurwitz numbers." J. Differential Geom. 98 (3) 375 - 423, November 2014.


Published: November 2014
First available in Project Euclid: 28 July 2014

zbMATH: 1315.53100
MathSciNet: MR3263522
Digital Object Identifier: 10.4310/jdg/1406552276

Rights: Copyright © 2014 Lehigh University

Vol.98 • No. 3 • November 2014
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