The Chow ring of the moduli space of curves of genus zero

TL;DR

This paper provides a simplified and explicit description of the Chow ring of the moduli space of genus zero curves, including a basis for Chow groups and duality, building on Keel's recursive algebra.

Contribution

It offers a new, simpler construction of the moduli space's intersection ring with fewer generators and relations, enhancing understanding of its algebraic structure.

Findings

Explicit basis for Chow groups

Duality between Chow groups in complementary degrees

Simpler presentation of the intersection ring

Abstract

After recalling several constructions of the moduli space of curves of genus zero by different people we give our alternative construction of the moduli space. This gives a simple description of the intersection ring of this space. We give a basis for the Chow groups and an explicit duality between the Chow groups in complementary degrees. There is a recursive description of this algebra by S. Keel. Our presentation is simpler in the sense that there are fewer generators and fewer relations and our description is explicit.