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# Communications in Number Theory and Physics

## Volume 7 (2013)

### Number 1

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

Pages: 125 – 143

DOI: http://dx.doi.org/10.4310/CNTP.2013.v7.n1.a4

#### Authors

#### Abstract

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 Schrödinger 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.