A new spin on Hurwitz theory and ELSV via theta characteristics
Abstract
We study spin Hurwitz numbers, which count ramified covers of the Riemann sphere with a sign coming from a theta characteristic. These numbers are known to be related to Gromov-Witten theory of K\"ahler surfaces and to representation theory of the Sergeev group, and are generated by BKP tau-functions. We use the latter interpretation to give polynomiality properties of these numbers and we derive a spectral curve which we conjecture computes spin Hurwitz numbers via a new type of topological recursion. We prove that this conjectural topological recursion is equivalent to an ELSV-type formula, expressing spin Hurwitz numbers in terms of the Chiodo class twisted by the -spin Witten class.
Keywords
Cite
@article{arxiv.2104.05697,
title = {A new spin on Hurwitz theory and ELSV via theta characteristics},
author = {Alessandro Giacchetto and Reinier Kramer and Danilo Lewański},
journal= {arXiv preprint arXiv:2104.05697},
year = {2024}
}
Comments
56 pages; v2: typos corrected, references updated, results unchanged