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The Moduli Space of Real Abelian Varieties with Level Structure

Published online by Cambridge University Press:  04 December 2007

Mark Goresky  and
Yung Sheng Tai
Mark Goresky
Affiliation:
School of Mathematics, Institute for Advanced Study, Princeton N.J., U.S.A. email: [email protected].
Yung Sheng Tai
Affiliation:
Department of Mathematics, Haverford College, Haverford PA, U.S.A.
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Abstract

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The moduli space of principally polarized Abelian varieties with real structure and with level N = 4m structure (with m≥1) is shown to coincide with the set of real points of a quasi-projective algebraic variety defined over ${\open Q}$, and to consist of finitely many copies of the quotient of the space GL(n, ${\open R}$)/O(N) (of positive definite symmetric matrices) by the principal congruence subgroup of level N in GL(n, ${\open Z}$).

Keywords

Abelian varietyreal algebraicsymmetric spacearithmetic groupanti-holomorphic involutionmoduli spaceComessatti lemmaBaily-Borel compactification
Type
Research Article
Information
Compositio Mathematica , Volume 139 , Issue 1 , October 2003 , pp. 1 - 27
Copyright
© 2003 Kluwer Academic Publishers