The Prym map of degree-7 cyclic coverings

TL;DR

This paper investigates the Prym map for degree-7 cyclic coverings over genus-2 curves, extending it to a compactified moduli space and establishing its generic finiteness and degree.

Contribution

It extends the Prym map to a partial compactification and proves it is generically finite of degree 10.

Findings

Prym map extends to a proper map on a partial compactification.

The Prym map is generically finite onto its image.

The degree of the Prym map is 10.

Abstract

We study the Prym map for degree-7 etale cyclic coverings over a curve of genus 2. We extend this map to a proper map on a partial compactification of the moduli space of such coverings, and prove that the Prym map is generically finite onto its image of degree 10.