The spectral curve of the Eynard-Orantin recursion via the Laplace transform

Details The spectral curve of the Eynard-Orantin recursion via the Laplace transform The spectral curve of the Eynard-Orantin recursion via the Laplace transform

2012-02-06

arxiv.org/abs/1202.1159v1

Mathematics

Algebraic Geometry

49 pages, 7 figures

Scientific paper

The Eynard-Orantin recursion formula provides an effective tool for certain enumeration problems in geometry. The formula requires a spectral curve and the recursion kernel. We present a uniform construction of the spectral curve and the recursion kernel from the unstable geometries of the original counting problem. We examine this construction using four concrete examples: Grothendieck's dessins d'enfants (or higher-genus analogue of the Catalan numbers), the intersection numbers of tautological cotangent classes on the moduli stack of stable pointed curves, single Hurwitz numbers, and the stationary Gromov-Witten invariants of the complex projective line.

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