Bielliptic ball quotient compactifications and lattices in PU(2, 1) with finitely generated commutator subgroup

Abstract

© Association des Annales de l'institut Fourier, 2017. We construct two infinite families of ball quotient compactifications birational to bielliptic surfaces. For each family, the volume spectrum of the associated noncompact finite volume ball quotient surfaces is the set of all positive integral multiples of 8/3 π2, i.e., they attain all possible volumes of complex hyperbolic 2-manifolds. The surfaces in one of the two families all have 2-cusps, so that we can saturate the entire volume spectrum with 2-cusped manifolds. Finally, we show that the associated neat lattices have infinite abelianization and finitely generated commutator subgroup. These appear to be the first known nonuniform lattices in PU(2, 1), and the first infinite tower, with this property.