Potential density of rational points on the variety of lines of a cubic fourfold

TL;DR

This paper proves that rational points are potentially dense on the variety of lines of a sufficiently general cubic fourfold over a number field, under certain genericity conditions, contributing to understanding rational points on algebraic varieties.

Contribution

It establishes potential density of rational points on these varieties with trivial canonical bundle and Picard group equal to , under Terasoma-type conditions, extending knowledge in algebraic geometry.

Findings

Potential density proven for general cubic fourfolds

Varieties have trivial canonical bundle and Picard group 

Results depend on Terasoma-type genericity conditions

Abstract

We prove the potential density of rational points on the variety of lines of a sufficiently general cubic fourfold defined over a number field, where ``sufficiently general'' means that a condition of Terasoma type is satisfied. These varieties have trivial canonical bundle and have geometric Picard group equal to $\mathbb{Z}$.