On the Chow ring of the stack of rational nodal curves

TL;DR

This paper computes the rational Chow ring of the stack of genus 0 nodal curves with up to 3 nodes, revealing its algebraic structure with explicit generators and relations.

Contribution

It provides the first explicit description of the Chow ring for this specific stack of rational nodal curves, including generators and relations.

Findings

The Chow ring is a Q-algebra with 10 generators and 11 relations.

Explicit presentation of the Chow ring structure.

Advances understanding of the intersection theory of rational nodal curves.

Abstract

The goal of this paper is to compute the rational Chow ring of the stack consisting of nodal curves of genus 0 with at most 3 nodes: it is a Q-algebra with 10 generators and 11 relations.