With cedram.org English français Home Overview Search for an article Submit a paper Informations for the authors Subscription Limited access - RUCHE Table of contents for this issue | Previous article | Next article Luca F. Di Cerbo; Matthew StoverBielliptic ball quotient compactifications and lattices in $\text{PU}(2, 1)$ with finitely generated commutator subgroup(Compactifications bi-elliptiques de quotients de la boule et réseaux dans $\mathrm{PU}(2,1)$ dont le sous-groupe dérivé est de type fini)Annales de l'institut Fourier, 67 no. 1 (2017), p. 315-328, doi: 10.5802/aif.3083 Article PDF Class. Math.: 32Q45, 14M27, 57M50Keywords: Ball quotients and their compactifications, volumes of complex hyperbolic manifolds Résumé - AbstractWe 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 $\frac{8}{3}\pi ^{2}$, 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 $\mathrm{PU}(2,1)$, and the first infinite tower, with this property. Bibliography[1] A. Ash, D. Mumford, M. Rapoport & Y.-S. Tai, Smooth compactifications of locally symmetric varieties, Cambridge Mathematical Library, Cambridge University Press, 2010 [2] A. Beauville, Complex algebraic surfaces, London Mathematical Society Student Texts 34, Cambridge University Press, 1996 [3] D. Cartwright, V. Koziarz & S.-K. 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