Abstract

Let (X, H) be a g-dimensional principally polarized abelian variety (p.p.a.v.) and Aut(X, H) its group of automorphisms, in this brief survey we describe some p.p.a.v. with large group of automorphism and their connections with p.p.a.v. of complex multiplication type. As any g-dimensional p.p.a.v. (X, H) admitting a non-trivial automorphism is a singular point of (the moduli space of complex g-dimensional p.p.a.v.), we give the description of some components of the singular locus and also we provide some examples to illustrate our main results. © Springer Science+Business Media B.V. 2008.