  Let $A$ be an abelian variety and $G$ a finite group of automorphisms of $A$
fixing the origin such that $A/G$ is smooth. The quotient $A/G$ can be seen as
a fibration over an abelian variety whose fibers are isomorphic to a product of
projective spaces. We classify how the fibers are glued in the case when the
fibers are isomorphic to a projective space and we prove that, in general, the
quotient $A/G$ is a fibered product of such fibrations.
