Mirror curve of orbifold Hurwitz numbers
Abstract
Edge-contraction operations form an effective tool in various graph enumeration problems, such as counting Grothendieck's dessins d'enfants and simple and double Hurwitz numbers. These counting problems can be solved by a mechanism known as topological recursion, which is a mirror B-model corresponding to these counting problems. We show that for the case of orbifold Hurwitz numbers, the mirror objects, i.e., the spectral curve and the differential forms on it, are constructed solely from the edge-contraction operations of the counting problem in genus and one marked point. This forms a parallelism with Gromov-Witten theory, where genus 0 Gromov-Witten invariants correspond to mirror B-model holomorphic geometry.
Keywords
Cite
@article{arxiv.1904.04903,
title = {Mirror curve of orbifold Hurwitz numbers},
author = {Olivia Dumitrescu and Motohico Mulase},
journal= {arXiv preprint arXiv:1904.04903},
year = {2019}
}
Comments
This preprint has 16 pages and 20 figures. This preprint together with arxiv: 1508.05922v3 (Journal of Algebra, vol. 494, January 2018) replaces arxiv:1508.05922v2. Grant acknowledgement added