Volumes of 3-ball quotients as intersection numbers

TL;DR

This paper provides explicit descriptions and presentations of 3-ball quotients, calculating their orbifold Euler characteristics, thereby advancing understanding of these geometric structures.

Contribution

It offers a detailed description and presentation of 3-ball quotients constructed by Couwenberg-Heckman-Looijenga, including explicit calculations of their orbifold Euler characteristics.

Findings

Explicit descriptions of 3-ball quotients.

Calculations of orbifold Euler characteristics.

Presentations in terms of generators and relations.

Abstract

We give an explicit description of the 3-ball quotients constructed by Couwenberg-Heckman-Looijenga, and deduce the value of their orbifold Euler characteristics. For each lattice, we also give a presentation in terms of generators and relations.