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Abelian varieties over \({\mathbb{C}}.\) (Notes by F. O. McGuinness). (English) Zbl 0604.14032
Arithmetic geometry, Pap. Conf., Storrs/Conn. 1984, 79-101 (1986).
[For the entire collection see Zbl 0596.00007.]
This paper is an excellent survey of the theory of abelian varieties over the field of complex numbers, from the analytic point of view. After recalling some general and basic facts about abelian varieties, the author discusses the following problem: isogenies and the equivalence relation associated to them, criteria to recognize when a complex torus is an abelian variety, the dual abelian variety, polarizations of abelian varieties and the moduli space of principally polarized abelian varieties. Although in general the proofs are omitted or only sketched, this article is a good introduction to the analytic theory of abelian varieties.
Reviewer: L.Bădescu

MSC:
14K20 Analytic theory of abelian varieties; abelian integrals and differentials
14K25 Theta functions and abelian varieties