Abelian approach to modular forms of neat 2-ball lattices: Dimension formulas

Rolf-Peter Holzapfel

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 13

MSC 2000

11G15 Complex multiplication and moduli of abelian varieties
11G18 Arithmetic aspects of modular and Shimura varieties
14H52 Elliptic curves
14J25 Special surfaces
20H05 Unimodular groups, congruence subgroups
ZDM: 32M15

In previous papers [HoEis], [Ho2000] we found neat Picard modular surfaces with abelian minimal model and, conversely, a divisor criterion on abelian surfaces A for such a situation. For the corresponding ball lattices $\Gamma$ we prove dimension formulas for modular forms depending only on the intersection graph of the image on A of the compactification divisor of the $\Gamma$-quotient surface.

Keywords:algebraic surfaces, Shimura varieties, arithmetic groups, Picard modular groups, unit ball, modular forms