Rational cohomology of $\mathcal M_{4,1}$

TL;DR

This paper calculates the rational cohomology of the moduli space of genus 4 curves with one marked point using a specialized topological method.

Contribution

It provides the first explicit computation of the rational cohomology for $\

Findings

Explicit rational cohomology groups for $\\mathcal{M}_{4,1}$ are obtained.

The computation employs Gorinov-Vassiliev's method.

Results enhance understanding of the topology of moduli spaces.

Abstract

We compute the rational cohomology of the moduli space $\mathcal{M}_{4,1}$ of non-singular genus $4$ curves with $1$ marked point, using Gorinov-Vassiliev's method.