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

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arxiv 1301.5580 v2 pith:GJHY47HR submitted 2013-01-23 math.AG math-phmath.MP

Motohico Mulase , Sergey Shadrin , Loek Spitz This is my paper · ORCID
classification math.AGmath-phmath.MP
keywords hurwitzcurvesnumbersspectralcasesdoubleschroedingerspin
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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 Schroedinger 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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  1. Quantum Curves in the Context of Symplectic Duality

    math-ph 2025-04 conditional novelty 6.0 of 10

    Quantum spectral curve operators for arbitrary base points can be derived by applying x-y and symplectic duality transformations to simpler spectral curves.

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