Compositio Mathematica

On the Rank of Picard Groups of Modular Varieties Attached to Orthogonal Groups

Jan Hendrik Bruinier a1
a1 University of Wisconsin-Madison, Department of Mathematics, Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706-1388, U.S.A. E-mail:

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bruinier jh   [Google Scholar] 


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.