Smooth quotients of principally polarized abelian varieties

Abstract

We give an explicit characterization of all principally polarized abelian varieties $(A,\Theta)$ such that there is a finite subgroup of automorphisms $G$ of $A$ that preserve the numerical class of $\Theta$, and such that the quotient variety $A/G$ is smooth. We also give a complete classification of smooth quotients of Jacobians of curves.