Institute of Mathematics and Informatics Bulgarian Academy of Sciences
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
