A new proof of Faber's intersection number conjecture

TL;DR

This paper presents a new proof of Faber's intersection number conjecture for the moduli space of curves, utilizing geometric and combinatorial methods involving double ramification cycles.

Contribution

It introduces a novel proof technique for Faber's conjecture based on straightforward geometric and combinatorial computations.

Findings

Proof confirms Faber's intersection number conjecture.

Method simplifies previous approaches to the conjecture.

Highlights the role of double ramification cycles in intersection theory.

Abstract

We give a new proof of Faber's intersection number conjecture concerning the top intersections in the tautological ring of the moduli space of curves $\M_g$. The proof is based on a very straightforward geometric and combinatorial computation with double ramification cycles.