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A new spin on Hurwitz theory and ELSV via theta characteristics

  • Alessandro Giacchetto [1] ; Reinier Kramer [1] ; Danilo Lewanski [2]
    1. [1] Max Planck Institute for Mathematics

      Max Planck Institute for Mathematics

      Kreisfreie Stadt Bonn, Alemania

    2. [2] Inst. Hautes Études Scientifiques (IHES), Paris, France
  • Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 5, 2025
  • Idioma: inglés
  • DOI: 10.1007/s00029-025-01077-y
  • Enlaces
  • Resumen

    • 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 Kähler 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.

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