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Title: Complex Hyperbolic Surfaces of Abelian Type
Authors: Holzapfel, R.
Keywords: Algebraic Curve
Elliptic Curve
Algebraic Surface
Shimura Variety
Arithmetic Group
Picard Modular Group
Gauß Numbers
Congruence Numbers
Negative Constant Curvature
Unit Ball
Kähler-Einstein Metrics
Issue Date: 2004
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 30, No 2-3, (2004), 207p-238p
Abstract: We call a complex (quasiprojective) surface of hyperbolic type, iff – after removing finitely many points and/or curves – the universal cover is the complex two-dimensional unit ball. We characterize abelian surfaces which have a birational transform of hyperbolic type by the existence of a reduced divisor with only elliptic curve components and maximal singularity rate (equal to 4). We discover a Picard modular surface of Gauß numbers of bielliptic type connected with the rational cuboid problem. This paper is also necessary to understand new constructions of Picard modular forms of 3-divisible weights by special abelian theta functions.
Description: 2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.
ISSN: 1310-6600
Appears in Collections:Volume 30 Number 2-3

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