On the Rank of Picard Groups of Modular Varieties Attached to Orthogonal Groups
We derive lower bounds for the rank of Picard groups of modular varieties associated with natural congruence subgroups of the orthogonal group of an even lattice of signature (2, l). As an example we consider the Siegel modular group of genus 2. The analytic part of this paper also leads to certain class number identities.
Key Words: Picard group; orthogonal group; class number.