On algebraic equivalences among the 27 Abel-Prym curves on a generic abelian 5-fold

TL;DR

This paper investigates algebraic relations among 27 Abel-Prym curves on a generic abelian 5-fold, revealing a 20-dimensional space of equivalences, thus deepening understanding of their algebraic structure.

Contribution

It establishes the dimension of the space of algebraic equivalences among the 27 Abel-Prym curves on a generic abelian 5-fold, a new result in algebraic geometry.

Findings

The space of algebraic equivalences has dimension 20.

There are specific algebraic relations among the 27 Abel-Prym curves.

The result applies to generic principally polarized abelian 5-folds.

Abstract

This article shows that on a generic principally polarized abelian variety of dimension five the $\mathbb{Q}$-vector space of algebraic equivalences among the 27 Abel-Prym curves has dimension 20.