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.

Theorems & Definitions (20)

• Theorem 1.1: Theorem 1.1 ALA - Theorem 1.1 Queso
• Theorem 1.2: Theorem 1.3 ALA
• Remark 1.3
• Theorem 1.4
• Theorem 1.5
• proof : Proof of Theorem \ref{['maintheorem2']}
• Remark 2.1
• Definition 3.1
• Proposition 3.2
• proof