Polynomials representing Eynard-Orantin invariants

TL;DR

This paper demonstrates how Eynard-Orantin invariants for certain genus zero plane curves can be expressed using polynomials derived from their local expansions, simplifying their computation.

Contribution

It introduces a polynomial representation for Eynard-Orantin invariants on a specific class of genus zero curves, providing a new computational approach.

Findings

Polynomials effectively represent invariants for genus zero curves.

Simplifies calculations of Eynard-Orantin invariants.

Applicable to many interesting curve examples.

Abstract

The Eynard-Orantin invariants of a plane curve are multilinear differentials 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 contains many interesting examples.