# Complex Hyperbolic Surfaces of Abelian Type

Serdica Mathematical Journal (2004)

- Volume: 30, Issue: 2-3, page 207-238
- ISSN: 1310-6600

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topHolzapfel, R.. "Complex Hyperbolic Surfaces of Abelian Type." Serdica Mathematical Journal 30.2-3 (2004): 207-238. <http://eudml.org/doc/219600>.

@article{Holzapfel2004,

abstract = {2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.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.},

author = {Holzapfel, R.},

journal = {Serdica Mathematical Journal},

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; algebraic curve; elliptic curve; algebraic surface; Shimura variety; arithmetic group; Picard modular group; Gauss numbers; congruence numbers; Kähler-Einstein metric; negative constant curvature; unit ball},

language = {eng},

number = {2-3},

pages = {207-238},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Complex Hyperbolic Surfaces of Abelian Type},

url = {http://eudml.org/doc/219600},

volume = {30},

year = {2004},

}

TY - JOUR

AU - Holzapfel, R.

TI - Complex Hyperbolic Surfaces of Abelian Type

JO - Serdica Mathematical Journal

PY - 2004

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 30

IS - 2-3

SP - 207

EP - 238

AB - 2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.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.

LA - eng

KW - 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; algebraic curve; elliptic curve; algebraic surface; Shimura variety; arithmetic group; Picard modular group; Gauss numbers; congruence numbers; Kähler-Einstein metric; negative constant curvature; unit ball

UR - http://eudml.org/doc/219600

ER -