Non-arithmetic lattices and the Klein quartic

TL;DR

This paper presents an algebraic geometric method to construct non-arithmetic ball quotients, linking their fundamental groups to the Klein quartic's automorphisms and related groups, expanding understanding of complex hyperbolic geometry.

Contribution

It introduces a new algebraic geometric construction of non-arithmetic ball quotients, connecting them to the Klein quartic's automorphism group and other known groups.

Findings

Established a relationship between orbifold fundamental groups and Klein quartic automorphisms.

Connected new constructions to existing groups by Barthel-Hirzebruch-Höfer and Couwenberg-Heckman-Looijenga.

Revealed geometric structures underlying certain non-arithmetic lattices.

Abstract

We give an algebro-geometric construction of some of the non-arithmetic ball quotients constructed by the author, Parker and Paupert. The new construction reveals a relationship between the corresponding orbifold fundamental groups and the automorphism group of the Klein quartic, and also with groups constructed by Barthel-Hirzebruch-H\"ofer and Couwenberg-Heckman-Looijenga.