Quantum curves for simple Hurwitz numbers of an arbitrary base curve

2013/03/29 by Liu, Xiaojun, Mulase, Motohico, Sorkin, Adam
#05C30 #11P21 #14N35 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 14H15 #Secondary: 81T30

paper · doi:10.48550/arxiv.1304.0015

Abstract

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.

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