Volumes of Picard modular surfaces

Matthew Stover
2011 Proceedings of the American Mathematical Society  
We show that the conjectural cusped complex hyperbolic 2-orbifolds of minimal volume are the two smallest arithmetic complex hyperbolic 2orbifolds. We then show that every arithmetic cusped complex hyperbolic 2-manifold of minimal volume covers one of these two orbifolds. We also give all minimal volume manifolds that simultaneously cover both minimal orbifolds.
doi:10.1090/s0002-9939-2011-10786-x fatcat:wl4o5ek4brcrfd3xnwytgm4bba