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.