Complex Hyperbolic Surfaces of Abelian Type

Holzapfel, 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 -