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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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