# A new spin on Hurwitz theory and ELSV via theta characteristics

@inproceedings{Giacchetto2021ANS, title={A new spin on Hurwitz theory and ELSV via theta characteristics}, author={Alessandro Giacchetto and Reinier Kramer and Danilo Lewa'nski}, year={2021} }

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 Kähler 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…

## 6 Citations

Relations for quadratic Hodge integrals via stable maps

- Mathematics
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. Following Faber-Pandharipande, we use the virtual localization formula for the moduli space of stable maps to P 1 to compute relations between Hodge integrals. We prove that certain generating…

Integrals of $\psi$-classes on twisted double ramification cycles and spaces of differentials

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We prove a closed formula for the integral of a power of a single ψ-class on strata of k-differentials. In many cases, these integrals correspond to intersection numbers on twisted double…

Genus one free energy contribution to the quartic Kontsevich model

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We prove a formula for the genus one free energy F (1) of the quartic Kontsevich model for arbitrary ramification by working out a boundary creation operator for blobbed topological recursion. We…

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We advertise elementary symmetric polynomials ei as the natural basis for generating series Ag,n of intersection numbers of genus g and n marked points. Closed formulae for Ag,n are known for genera…

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Abstract. We generalise a result of Kazarian regarding Kadomtsev-Petviashvili integrability for single Hodge integrals to general cohomological field theories related to Hurwitz-type counting…

Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto-Kramer-Lewanski conjecture

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In this paper, we discuss the properties of the generating functions of spin Hurwitz numbers. In particular, for spin Hurwitz numbers with arbitrary ramification profiles, we construct the weighed…

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