The (almost) integral Chow ring of $\overline{\mathcal{M}}_3$

TL;DR

This paper completes the computation of the (almost) integral Chow ring of the moduli stack of stable genus 3 curves, providing a detailed algebraic description with specific coefficients.

Contribution

It presents the first complete calculation of the Chow ring of rac{rac{ ext{M}}_3$ with rac{rac{ ext{Z}}[1/6]-coefficients, advancing understanding of algebraic cycles on moduli spaces.

Findings

Chow ring of rac{rac{ ext{M}}_3$ computed with rac{rac{ ext{Z}}[1/6] coefficients.

Explicit generators and relations for the Chow ring established.

Completes the series of papers on the algebraic structure of rac{rac{ ext{M}}_3$.

Abstract

This paper is the fourth in a series of four papers aiming to describe the (almost integral) Chow ring of $\overline{\mathcal{M}}_3$, the moduli stack of stable curves of genus $3$. In this paper, we finally compute the Chow ring of $\overline{\mathcal{M}}_3$ with $\mathbb{Z}[1/6]$-coefficients.