String and dilaton equations for counting lattice points in the moduli space of curves
Algebraic Geometry
2011-02-09 v2 Mathematical Physics
math.MP
Abstract
We prove that the Eynard-Orantin symplectic invariants of the curve xy-y^2=1 are the orbifold Euler characteristics of the moduli spaces of genus g curves. We do this by associating to the Eynard-Orantin invariants of xy-y^2=1 a problem of enumerating covers of the two-sphere branched over three points. This viewpoint produces new recursion relations---string and dilaton equations---between the quasi-polynomials that enumerate such covers.
Cite
@article{arxiv.0905.4141,
title = {String and dilaton equations for counting lattice points in the moduli space of curves},
author = {Paul Norbury},
journal= {arXiv preprint arXiv:0905.4141},
year = {2011}
}
Comments
23 pages