An effective recursion formula for computing intersection numbers

TL;DR

This paper introduces a new recursion formula that simplifies the computation of intersection numbers on the moduli space of curves, relying solely on genus induction.

Contribution

It presents a novel recursion formula for intersection indices that depends only on genus, streamlining calculations on the moduli space of curves.

Findings

Provides an effective recursive method for intersection number computation

Simplifies calculations by depending only on genus

Enhances understanding of moduli space intersection theory

Abstract

We prove a new effective recursion formula for computing all intersection indices (integrals of $\psi$ classes) on the moduli space of curves, inducting only on the genus.