A decomposition of the Jacobian of a Humbert-Edge curve

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.

arXiv comment9 pages, comments welcome! To appear in Contemporary Mathematics

Cited by in corpus (2)

• Geometric aspects on Humbert-Edge's curves of type 5, Kummer surfaces and hyperelliptic curves of genus 2
• Decomposition of jacobians of generalized Fermat curves