An abelian variety polarization on an abelian variety 
over a field 
is an isogeny 
that, over an algebraic
closure, is induced by an ample line bundle 
via
 |
where 
is translation by 
.
It is principal when it is an isomorphism. The ample line bundle need not itself descend to 
(Milne 2008). Principally polarized abelian varieties
are parametrized by the Siegel moduli variety.
