Chow rings of moduli spaces of genus 0 curves with collisions

TL;DR

This paper provides new presentations of the Chow rings of simplicially stable spaces, a class of compactifications of genus 0 moduli spaces, extending known results and offering alternative proofs for classical cases.

Contribution

It introduces new presentations of Chow rings for simplicially stable spaces in genus 0, generalizing existing results and providing a novel proof for Keel's presentation.

Findings

New presentations of Chow rings for simplicially stable spaces.

Extension of Keel's results to broader classes of moduli spaces.

Simplification of proofs for known Chow ring structures.

Abstract

Introduced in [BB], simplicially stable spaces are alternative compactifications of $\mathcal{M}_{g,n}$ generalizing Hassett's moduli spaces of weighted stable curves. We give presentations of the Chow rings of these spaces in genus $0$ using techniques developed by the author in [New25]. When considering the special case of $\overline{\mathcal{M}}_{0,n}$, this gives a new proof of Keel's presentation of $\operatorname{CH}(\overline{\mathcal{M}}_{0,n})$.