The Chow Ring of the Moduli Space of Abelian Threefolds

TL;DR

This paper determines the structure of the Chow ring of a specific compactification of the moduli space of abelian threefolds, providing insights into its algebraic cycles and their relations.

Contribution

It explicitly computes the Chow ring of the Delaunay-Voronoi compactification of the moduli space of abelian threefolds, a previously uncharacterized structure.

Findings

Chow ring structure of $ ilde{\ m A}_3$ determined

Comparison with Chow ring of genus 3 curves conducted

Use of equivariant classes on level coverings for computation

Abstract

In this paper we determine the structure of the Chow ring of the Delaunay-Voronoi compactification $\tilde{\cal A}_3$ of the moduli space of principally polarized abelian threefolds. This compactification was introduced by Namikawa and studied by Tsushima. We use equivariant classes on level coverings of $\tilde{\cal A}_3$. We also compare this ring with the Chow ring of the moduli space of stable genus 3 curves as determined by Faber.