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Siegel moduli schemes and their compactifications over \(\mathbb C\). (English) Zbl 0603.14027
Arithmetic geometry, Pap. Conf., Storrs/Conn. 1984, 231-251 (1986).
[For the entire collection see Zbl 0596.00007.]
The paper under review is intended to be an elementary, geometric introduction to the moduli space of abelian varieties and their compactifications. The paper begins with generalities on the moduli functors and their coarse moduli spaces. Then the transcendental aspects of the theory are presented. Two kinds of compactifications are discussed in the realm of matrices: the Satake compactification and the toroidal compactification (in the Siegel case). In the last part of the paper one explains how these things occur in Faltings’ finiteness theorem. In general the technical details are omitted.
Reviewer: Lucian Bădescu

14K10 Algebraic moduli of abelian varieties, classification
32G13 Complex-analytic moduli problems
14D20 Algebraic moduli problems, moduli of vector bundles