On the geometry of thin exceptional sets in Manin's Conjecture

TL;DR

This paper investigates whether the exceptional set in Manin's Conjecture, which predicts the distribution of rational points, is a thin set, contributing to understanding the structure of these sets in algebraic geometry.

Contribution

It provides a detailed analysis of the exceptional set in Manin's Conjecture, exploring its potential thinness and geometric properties.

Findings

The exceptional set may be a thin set under certain conditions.

Characterization of the geometric structure of the exceptional set.

Implications for the distribution of rational points on algebraic varieties.

Abstract

Manin's Conjecture predicts the rate of growth of rational points of a bounded height after removing those lying on an exceptional set. We study whether the exceptional set in Manin's Conjecture is a thin set.