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Quantum curves for simple Hurwitz numbers of an arbitrary base curve

Various generating functions of simple Hurwitz numbers of the projective line are known to satisfy many properties. They include a heat equation, the Eynard-Orantin topological recursion, an infinite-order differential equation called a quantum curve equation, and a Schroedinger like partial differential equation. In this paper we generalize these properties to simple Hurwitz numbers with an arbitrary base curve.

preprint2013arXivOpen access
Xiaojun LiuMotohico MulaseAdam Sorkin
math-phmath.MPmath.AG
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Xiaojun LiuMotohico MulaseAdam Sorkin

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