Hyperbolic Planes
Abstract
Description
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.
29 pages (11 pt), dvi file available from the author by request to hunt@mathematik.uni-kl.de , LaTeX v 2.09
29 pages (11 pt), dvi file available from the author by request to hunt@mathematik.uni-kl.de , LaTeX v 2.09