Cusps of Picard modular surfaces
classification
🧮 math.GT
math.NT
keywords
cuspsmodularpicardsurfacesarithmeticanalogueclassescommensurability
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We determine the number of cusps of minimal Picard modular surfaces. The proof also counts cusps of other Picard modular surfaces of arithmetic interest. Consequently, for each N > 0 there are finitely many commensurability classes of nonuniform arithmetic lattices in SU(2, 1) that contain an N-cusped surface. We also discuss a higher-rank analogue.
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