A combinatorial proof of the $\lambda_g$ conjecture in genus 2

TL;DR

This paper presents a straightforward combinatorial proof of the $1$ conjecture for genus 2, utilizing boundary strata and classical relations in moduli space to establish the result.

Contribution

It provides the first simple combinatorial proof of the $1$ conjecture in genus 2, leveraging boundary class descriptions and standard recursive formulas.

Findings

Proof confirms the $1$ conjecture in genus 2.

Uses boundary strata and classical equations for the proof.

Simplifies previous approaches to the conjecture.

Abstract

We give a simple combinatorial proof of the $\lambda_g$ conjectue in genus 2. We use a description of the class $\lambda_2$ as a linear combination of boundary strata, and show the conjecture follows inductively from applications of the projection formula, string equation, and dilaton equation.