The cohomology of $\mathcal{M}_{0,n}$ as an FI-module

TL;DR

This paper examines the cohomology of the moduli space of genus zero curves with n marked points through the lens of FI-modules, providing a new perspective on known symmetric group representations.

Contribution

It applies the FI-module framework to the cohomology of m, offering a novel approach to understanding its symmetric group actions.

Findings

Reveals the structure of cohomology groups as FI-modules.

Recovers known symmetric group representation results.

Provides a new perspective on moduli space cohomology.

Abstract

In this paper we revisit the cohomology groups of the moduli space of $n$-pointed curves of genus zero using the FI-module perspective introduced by Church-Ellenberg-Farb. We recover known results about the corresponding representations of the symmetric group.