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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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


Authors: R. Kramer, D. Lewanski, A. Popolitov and S. Shadrin
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 14H30; Secondary 14H10, 53D45, 14N10
DOI: https://doi.org/10.1090/tran/7793
Published electronically: February 25, 2019
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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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Additional Information

R. Kramer
Affiliation: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Postbus 94248, 1090 GE Amsterdam, The Netherlands
Email: R.Kramer@uva.nl

D. Lewanski
Affiliation: Max Planck Institute for Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
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
Email: popolit@gmail.com

S. Shadrin
Affiliation: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Postbus 94248, 1090 GE Amsterdam, The Netherlands
Email: S.Shadrin@uva.nl

DOI: https://doi.org/10.1090/tran/7793
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.
Article copyright: © Copyright 2019 American Mathematical Society