# Abelian variety

From Groupprops

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).