Volumes of Picard modular surfaces
classification
🧮 math.GT
keywords
minimalorbifoldscomplexhyperbolicvolumearithmeticcuspedconjectural
read the original abstract
We show that the conjectural cusped complex hyperbolic 2-orbifolds of minimal volume are the two smallest arithmetic complex hyperbolic 2-orbifolds. 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.
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