# Smooth quotients of principally polarized abelian varieties

## TL;DR

This paper characterizes and classifies principally polarized abelian varieties and Jacobian quotients that admit smooth quotients under finite automorphism groups, providing explicit criteria and comprehensive classifications.

## Contribution

It offers an explicit characterization of abelian varieties with smooth quotients and a complete classification of smooth Jacobian quotients, advancing understanding of automorphism actions.

## Key findings

- Identifies conditions for smooth quotients of abelian varieties.
- Provides a full classification of smooth Jacobian quotients.
- Characterizes automorphism groups preserving polarization classes.

## 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.