Volumes of Picard modular surfaces

DOI10.1090/S0002-9939-2011-10786-XzbMath1301.22005arXiv1005.4436MaRDI QIDQ3092830

Matthew Stover

Publication date: 11 October 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.4436

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Structure of modular groups and generalizations; arithmetic groups (11F06) Linear algebraic groups over the reals, the complexes, the quaternions (20G20)

Related Items (13)

The densest lattices in \(\mathrm{PGL}_3(\mathbb Q_2)\) ⋮ A presentation for the Eisenstein-Picard modular group in three complex dimensions ⋮ Unnamed Item ⋮ Presentations for cusped arithmetic hyperbolic lattices ⋮ Hurwitz ball quotients ⋮ Rigid surfaces arbitrarily close to the Bogomolov--Miyaoka--Yau line ⋮ Classification and arithmeticity of toroidal compactifications with \(3\overline{c}_2=\overline{c}_1^2=3\) ⋮ Counting and equidistribution in Heisenberg groups ⋮ On volumes of complex hyperbolic orbifolds ⋮ On Spherical CR Uniformization of 3-Manifolds ⋮ A classification of \(\mathbb{R}\)-Fuchsian subgroups of Picard modular groups ⋮ Cusp and b_1 growth for ball quotients and maps onto Z with finitely generated kernel ⋮ Residually finite lattices in \(\widetilde{\mathrm{PU}(2,1)}\) and fundamental groups of smooth projective surfaces

Uses Software

• Magma

Cites Work

• Enumeration of the 50 fake projective planes
• Fake projective planes
• Volumes of S-arithmetic quotients of semi-simple groups. With an appendix by Moshe Jarden and Gopal Prasad
• Finiteness theorems for discrete subgroups of bounded covolume in semi- simple groups
• An elementary account of Selberg's lemma
• The Magma algebra system. I: The user language
• On the volumes of cusped, complex hyperbolic manifolds and orbifolds
• The geometry of the Eisenstein-Picard modular group
• On volumes of arithmetic quotients of PO (n , 1)^° , n odd
• Braids, hypergeometric functions, and lattices
• Compact hyperbolic 4-manifolds of small volume
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