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

Published online by Cambridge University Press:  04 December 2007

Jan Hendrik Bruinier
Jan Hendrik Bruinier
Affiliation:
University of Wisconsin-Madison, Department of Mathematics, Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706-1388, U.S.A. E-mail: [email protected]
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Abstract

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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.

Keywords

Picard grouporthogonal groupclass number
Type
Research Article
Information
Compositio Mathematica , Volume 133 , Issue 1 , August 2002 , pp. 49 - 63
Copyright
© 2002 Kluwer Academic Publishers