Prym varieties of triple coverings

TL;DR

This paper characterizes Prym varieties arising from triple coverings of curves, establishing conditions under which they are principally polarized and exploring their properties and moduli.

Contribution

It provides a complete characterization of Prym varieties for triple coverings, focusing on non-cyclic, etale cases with genus 2 base curves, and studies their properties.

Findings

Prym varieties are principally polarized if and only if the covering is non-cyclic, etale, and the base curve has genus 2.

The paper investigates properties and moduli of these Prym varieties.

Provides criteria for when Prym varieties of triple coverings are principally polarized.

Abstract

We show that the Prym variety associated to a triple covering f: Y --> X of curves is principally polarized of dimension > 1, if and only if f is non-cyclic, etale and X is of genus 2. We investigate some properties of these Prym varieties and their moduli.