On exceptional sets in Manin's Conjecture

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.

An incorrect statement of Proposition 3.17 was fixed. A minor issue in the construction of thin sets in Section 6.1 was addressed. To appear in Research in the Mathematical Sciences