1202.1159 (Olivia Dumitrescu et al.)

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

Olivia Dumitrescu, Motohico Mulase, Brad Safnuk, Adam Sorkin

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.

View original: http://arxiv.org/abs/1202.1159