Department of Mathematics
The spectral curve of the Eynard-Orantin recursion via the Laplace transform
- Author(s): Dumitrescu, Olivia
- Mulase, Motohico
- Safnuk, Brad
- Sorkin, Adam
- et al.
Published Web Locationhttps://arxiv.org/pdf/1202.1159.pdf
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.