Abelian variety

This article defines a property that can be evaluated for an algebraic group. it is probably not a property that can directly be evaluated, or make sense, for an abstract group|View other properties of algebraic groups

Definition

An abelian variety is an algebraic group that, viewed as an algebraic variety, is a complete variety.

Examples

• Any elliptic curve group
• The Albanese variety, Picard variety, and intermediate Jacobian (all starting from a complete variety, such as a complex torus, can assign an algebraic group structure to it functorially).