# Etale double covers of cyclic p-gonal covers

## TL;DR

This paper investigates the Galois groups of certain covers in algebraic geometry and explores relationships between Prym varieties and Jacobians, extending known constructions in the field.

## Contribution

It computes Galois groups of specific covers and establishes new relations between Prym varieties and Jacobians, generalizing the trigonal construction.

## Key findings

- Galois groups of the covers are explicitly computed.
- Relations between Prym varieties and Jacobians are established.
- The work generalizes the trigonal construction.

## Abstract

This paper computes the Galois group of the Galois cover of the composition of an \'etale double cover of a cyclic $p$-gonal cover for any prime $p$. Moreover a relation between some of its Prym varieties and the Jacobian of a subcover is given. In a sense this generalizes the trigonal construction.