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A new spin on Hurwitz theory and ELSV via theta characteristics
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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.
Forward citations
Cited by 2 Pith papers
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Spin refinement of moduli spaces of residueless meromorphic differentials and the BKP hierarchy
The reduced DR hierarchy built from spin-weighted strata of residueless meromorphic differentials with two zeros equals the BKP hierarchy up to an explicit coordinate transformation.
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The bilinear fermionic form for KP and BKP hierarchies
A lifting-operator identity determines fermionic two-point functions from one-point functions for KP and BKP tau-functions, yielding closed formulas for the r-spin and BGW models.
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