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Siegel Moduli Schemes and Their Compactifications over ℂ

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Arithmetic Geometry

Abstract

The purpose of this chapter is to give a brief introduction to the moduli spaces of abelian varieties and their compactification. Only the geometric aspects of the theory are discussed. The arithmetic side is left untouched. The Satake and toroidal compactification are described within the realm of matrices. Although the theory looks more elementary and explicit, this approach also tends to obscure its group-theoretic nature (see [B-B], [SC] for the general case). The readers interested in a deeper pursuit of this subject may find more references in [GIT] and [Fr].

Supported in part by NSF grant MCS-8108814 (A03)

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Authors
  1. Ching-Li Chai
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Connecticut, Storrs, CT, 06268, USA

    Gary Cornell

  2. Department of Mathematics, Boston University, Boston, MA, 02215, USA

    Joseph H. Silverman

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© 1986 Springer-Verlag New York Inc.

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Chai, CL. (1986). Siegel Moduli Schemes and Their Compactifications over ℂ. In: Cornell, G., Silverman, J.H. (eds) Arithmetic Geometry. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8655-1_9

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  • DOI: https://doi.org/10.1007/978-1-4613-8655-1_9

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8657-5

  • Online ISBN: 978-1-4613-8655-1

  • eBook Packages: Springer Book Archive

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