Varieties with too many rational points

TL;DR

This paper studies Fano varieties over number fields that contain subvarieties with a large number of rational points, comparable to the total points on the entire variety, highlighting unusual distribution patterns.

Contribution

It introduces a new perspective on the distribution of rational points on Fano varieties by identifying subvarieties with unexpectedly high point counts.

Findings

Identification of subvarieties with high rational point density

Comparison of point counts between subvarieties and the entire variety

Insights into the distribution patterns of rational points

Abstract

We investigate Fano varieties defined over a number field that contain subvarieties whose number of rational points of bounded height is comparable to the total number on the variety.