Non-arithmetic ball quotients from a configuration of elliptic curves in an Abelian surface

TL;DR

This paper constructs new non-arithmetic ball quotients from Abelian surfaces, providing an alternative, computer-independent method to previously known lattices, and compares these with existing ones in the literature.

Contribution

It introduces a novel, explicit construction of non-arithmetic ball quotients via branched covers of Abelian surfaces, independent of computational methods.

Findings

Constructed non-arithmetic ball quotients from Abelian surfaces.

Provided an alternative, computer-free construction of certain lattices.

Compared new lattices with those previously documented in the literature.

Abstract

We construct some non-arithmetic ball quotients as branched covers of a quotient of an Abelian surface by a finite group, and compare them with lattices that previously appear in the literature. This gives an alternative construction, which is independent of the computer, of some lattices constructed by the author with Parker and Paupert.