abelian variety
projective abelian algebraic group
elliptic curve
a smooth projective curve of genus 1 equipped with a rational basepoint
Abelian surface
A 2-dimensional complex projective manifold carrying an abelian group structure
Albanese variety
generalisation of Jacobian variety
dual abelian variety
abelian variety that is the moduli space of degree 0 line bundles on another abelian variety