In this paper we consider a special class of arithmetic quotients of bounded
symmetric domains which can roughly be described as higher- dimensional
analogues of the Hilbert modular varities. The algebraic groups are defined as
the unitary groups over two-dimensional right vector spaces over a division
algebra with involution. If d denotes the degree of the division algebra,
then d=1 is essentially just case giving rise to Hilbert modular varieties.
We determine the class number (number of cusps) of the arithmetic quotients,
and find inter- esting modular subvarities whos existence derives from the
algebraic structure of the division algebras. Also the moduli interpretation,
given by Shimuras theory, is described.Comment: 29 pages (11 pt), dvi file available from the author by request to
[email protected] , LaTeX v 2.0
