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arXiv · 2104.05697

A new spin on Hurwitz theory and ELSV via theta characteristics

Alessandro Giacchetto·Reinier Kramer·Danilo Lewański
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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 $2$-spin Witten class.

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Alessandro Giacchetto, Reinier Kramer, Danilo Lewański. 2021-04-12. A new spin on Hurwitz theory and ELSV via theta characteristics. https://arxiv.org/abs/2104.05697

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