Fibrations associated to smooth quotients of abelian varieties

Abstract

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.