Polynomials representing Eynard-Orantin invariants

Abstract

The Eynard-Orantin invariants of a plane curve are multidifferentials on the curve. For a particular class of genus zero plane curves these invariants can be equivalently expressed in terms of simpler expressions given by polynomials obtained from an expansion of the Eynard-Orantin invariants around a point on the curve. This class of curves governs many interesting enumerative problems in geometry including counting lattice points in the moduli space of curves and the Gromov-Witten invariants of the 2-sphere. © 2012. Published by Oxford University Press. All rights reserved.