# A decomposition of the Jacobian of a Humbert-Edge curve

## TL;DR

This paper studies the Jacobian of Humbert-Edge curves, showing it can be decomposed into Prym-Tyurin varieties and analyzing the structure of the related isogeny.

## Contribution

It provides a novel decomposition of the Jacobian of Humbert-Edge curves into Prym-Tyurin varieties and computes the kernel of the associated isogeny.

## Key findings

- Jacobian decomposed into Prym-Tyurin varieties
- Kernel of the isogeny explicitly computed
- Enhanced understanding of the curve's geometric structure

## Abstract

A \textit{Humbert-Edge curve of type} $n$ is a non-degenerate smooth complete intersection of $n-1$ diagonal quadrics. Such a curve has an interesting geometry since it has a natural action of the group $(\mathbb{Z}/2\mathbb{Z})^n$. We present here a decomposition of its Jacobian variety as a product of Prym-Tyurin varieties, and we compute the kernel of the corresponding isogeny.