Sho Tanimoto: Some updates on thin exceptional sets in Manin’s conjecture

Abstract

Manin’s conjecture predicts the asymptotic formula for the counting function of rational points on a smooth rationally connected variety after removing the contribution from an exceptional set. Emmanuel Peyre was the first to suggest that this exceptional set should be a thin set, and in my joint work with Brian Lehmann and Akash Sengupta, we produced a conjectural description of this exceptional set and prove that it is indeed a thin set using techniques from the minimal model program. I have talked about this work for several conferences so that many people might have listened to this story. Taking this opportunity I will talk about several remarks about exceptional sets mainly focusing on possible extensions of our results to arbitrary big divisors.