Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1737

 Title: Complex Hyperbolic Surfaces of Abelian Type Authors: Holzapfel, R. Keywords: Algebraic CurveElliptic CurveAlgebraic SurfaceShimura VarietyArithmetic GroupPicard Modular GroupGauß NumbersCongruence NumbersNegative Constant CurvatureUnit BallKähler-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. URI: http://hdl.handle.net/10525/1737 ISSN: 1310-6600 Appears in Collections: Volume 30 Number 2-3

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