Chow ring of the stack of plane nodal curves

TL;DR

This paper calculates the rational Chow ring of the moduli stack of plane nodal curves of fixed degree, expressing it through tautological classes, and extends existing results to G-equivariant settings.

Contribution

It provides a detailed computation of the Chow ring for a specific moduli stack and generalizes Vial's results to G-equivariant contexts.

Findings

Chow ring of the moduli stack is explicitly computed.

Extension of Vial's results to G-equivariant settings.

Provides new tools for studying tautological classes in algebraic geometry.

Abstract

We compute the rational Chow ring of the moduli stack of planar nodal curves of fixed degree and express it in terms of tautological classes. Along the way, we extend Vial's results on Chow groups of Brauer-Severi varieties to $G$-equivariant settings.