On the cohomology of moduli spaces of (weighted) stable rational curves

TL;DR

This paper presents a recursive algorithm to compute the symmetric group representation character of the cohomology of moduli spaces of stable rational curves, revealing new formulas for character length using Hassett's weighted stable curves.

Contribution

It introduces a novel recursive algorithm for cohomology character computation and derives a formula for maximum character length, leveraging Hassett's weighted stable curves.

Findings

Algorithm effectively computes cohomology characters

Derived a formula for maximum character length

Connected cohomology to weighted stable curves

Abstract

We give a recursive algorithm for computing the character of the cohomology of the moduli space $\Mmb_{0,n}$ of stable $n$-pointed genus zero curves as a representation of the symmetric group $\Sg_n$ on $n$ letters. Using the algorithm we can show a formula for the maximum length of this character. Our main tool is connected to the moduli spaces of weighted stable curves introduced by Hassett.