Line bundles of type (1,,,1,2,,,2,4,,,4) on Abelian Varieties

Abstract

We show birationality of the morphism associated to line bundles $L$ of type $(1,...,1,2,...,2,4,...,4)$ on a generic $g-$dimensional abelian variety into its complete linear system such that $h^0(L)=2^g$. When $g=3$, we describe the image of the abelian threefold and from the geometry of the moduli space $SU_C(2)$ in the linear system $|2\theta_C|$, we obtain analogous results in $\p H^0(L)$.