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

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- by R. Kramer, D. Lewanski, A. Popolitov and S. Shadrin PDF
- Trans. Amer. Math. Soc.
**372**(2019), 4447-4469 Request permission

## 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.## References

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## Additional Information

**R. Kramer**- Affiliation: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Postbus 94248, 1090 GE Amsterdam, The Netherlands
- MR Author ID: 1245081
- Email: R.Kramer@uva.nl
**D. Lewanski**- Affiliation: Max Planck Institute for Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
- MR Author ID: 1140181
- Email: ilgrillodani@mpim-bonn.mpg.de
**A. Popolitov**- Affiliation: Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden; Institute for Information Transmission Problems, Moscow 127994, Russia; and ITEP, Moscow 117218, Russia
- MR Author ID: 1063503
- Email: popolit@gmail.com
**S. Shadrin**- Affiliation: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Postbus 94248, 1090 GE Amsterdam, The Netherlands
- MR Author ID: 680371
- Email: S.Shadrin@uva.nl
- Received by editor(s): March 28, 2017
- Received by editor(s) in revised form: September 14, 2018
- Published electronically: February 25, 2019
- Additional Notes: The authors were supported by the Netherlands Organization for Scientific Research.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**372**(2019), 4447-4469 - MSC (2010): Primary 14H30; Secondary 14H10, 53D45, 14N10
- DOI: https://doi.org/10.1090/tran/7793
- MathSciNet review: 4009392