The spectral curve and the Schrödinger equation of double Hurwitz numbers and higher spin structures

  title={The spectral curve and the Schr{\"o}dinger equation of double Hurwitz numbers and higher spin structures},
  author={M. Mulase and S. Shadrin and L. Spitz},
  journal={Communications in Number Theory and Physics},
We derive the spectral curves for q-part double Hurwitz numbers, r-spin simple Hurwitz numbers, and arbitrary combinations of these cases, from the analysis of the unstable (0, 1)-geometry. We quantize this family of spectral curves and obtain the Schrodinger equations for the partition function of the corresponding Hurwitz problems. We thus confirm the conjecture for the existence of quantum curves in these generalized Hurwitz number cases. 
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