Conjectural relations in the tautological ring of $\bar{M}_{g,n}$

TL;DR

This paper introduces a broad class of conjectural relations in the tautological ring of the moduli space of stable curves, extending known relations and providing new insights into its intersection theory.

Contribution

It generalizes the Faber-Zagier relations, proposing a large new family of conjectural relations in the tautological ring of ar{M}_{g,n}.

Findings

Proposes a large class of conjectural relations in ar{M}_{g,n}

Extends and generalizes Faber-Zagier relations

Provides a framework for future verification and exploration

Abstract

We describe a very large class of conjectural relations in the tautological ring of the moduli space $\bar{M}_{g,n}$ of stable curves of genus $g$ with $n$ marked points, extending and generalizing the Faber-Zagier relations. These notes are loosely based on informal talks given by the author at the workshop at KTH Stockholm on "The moduli space of curves and its intersection theory" in April 2012.