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arXiv · 1703.06725

Towards an orbifold generalization of Zvonkine's $r$-ELSV formula

Reinier Kramer·Danilo Lewanski·Alexandr Popolitov·Sergey Shadrin
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Abstract

We perform a key step towards the proof of Zvonkine's conjectural $r$-ELSV formula that relates Hurwitz numbers with completed $(r+1)$-cycles to the geometry of the moduli spaces of the $r$-spin structures on curves: we prove the quasi-polynomiality property prescribed by Zvonkine's conjecture. Moreover, we propose an orbifold generalization of Zvonkine's conjecture and prove the quasi-polynomiality property in this case as well. In addition to that, we study the $(0,1)$- and $(0,2)$-functions in this generalized case and we show that these unstable cases are correctly reproduced by the spectral curve initial data.

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Reinier Kramer, Danilo Lewanski, Alexandr Popolitov, Sergey Shadrin. 2017-03-20. Towards an orbifold generalization of Zvonkine's $r$-ELSV formula. https://doi.org/10.1090/tran%2F7793

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