A semiabelian variety is a connected algebraic group 
fitting into an exact
sequence
 |
where 
is an Abelian variety and 
is a nonnegative integer.
This complex-field formulation describes an extension of
an Abelian variety by an algebraic
torus. For 
it is an Abelian variety, and when 
is a point it is a torus. The quasi-Albanese
variety is the universal semiabelian target for based algebraic maps from a smooth
quasi-projective variety.
