Fibrations associated to smooth quotients of abelian varieties

TL;DR

This paper studies smooth quotients of abelian varieties by finite automorphism groups, classifying fiber structures and showing that such quotients are fibered products of simpler fibrations.

Contribution

It classifies the fiber gluing in smooth quotients of abelian varieties and proves that these quotients are fibered products of fibrations with projective space fibers.

Findings

Classified fiber gluing in smooth quotients when fibers are projective spaces

Proved that quotients are fibered products of such fibrations

Described the structure of quotients as fibrations over 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.