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Mirror symmetry for orbifold Hurwitz numbers

Algebraic Geometry 2014-08-13 v1 High Energy Physics - Theory Mathematical Physics math.MP

Abstract

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 [C3/(Z/rZ)]. Finally, we prove that the mirror model to orbifold Hurwitz numbers admits a quantum curve.

Keywords

Cite

@article{arxiv.1301.4871,
  title  = {Mirror symmetry for orbifold Hurwitz numbers},
  author = {Vincent Bouchard and Daniel Hernandez Serrano and Xiaojun Liu and Motohico Mulase},
  journal= {arXiv preprint arXiv:1301.4871},
  year   = {2014}
}

Comments

39 pages, 2 figures

R2 v1 2026-06-21T23:12:50.727Z