On exceptional sets in Manin's Conjecture

TL;DR

This survey explores the geometric aspects of Manin's Conjecture, focusing on the recent conjectural description of the exceptional set and providing explicit computations in various examples.

Contribution

It offers a detailed description of the exceptional set in Manin's Conjecture and computes it in numerous cases, advancing understanding of its structure.

Findings

Explicit descriptions of the exceptional set in multiple examples

Verification of the conjectural description in specific cases

Enhanced understanding of the geometric nature of the exceptional set

Abstract

In this survey paper we study Manin's Conjecture from a geometric perspective. The focus of the paper is the recent conjectural description of the exceptional set in Manin's Conjecture due to Lehmann-Sengupta-Tanimoto. After giving an extensive background, we give a precise description of this set and compute it in many examples.