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.
