On the tautological ring of $M_{g,n}$

TL;DR

This paper explores the structure of the tautological ring of moduli spaces of pointed smooth curves, proposing conjectures analogous to Faber's for these spaces.

Contribution

It formulates and verifies conjectures about the tautological ring of $M_{g,n}$, extending Faber's conjectures to the case of pointed curves.

Findings

Proposes analogues of Faber's conjectures for $M_{g,n}$

Checks the validity of these conjectures in specific cases

Provides evidence supporting the conjectural structure of the tautological ring

Abstract

We state and check the analogue of Faber's conjectures for the tautological ring of the moduli spaces $M_{g,n}$ of $n$-pointed smooth curves of genus $g$.