Polarization (reviewed)

A polarization on an abelian variety is an isogeny to its dual abelian variety that is symmetric with respect to double-duality for abelian varieties and for which the pullback of the Poincaré bundle along the associated graph morphism is ample.

Any abelian variety admits at least one polarization. In fact, over $\C$ the existence of a polarization distinguishes abelian varieties among complex tori.