Sections of Fano Fibrations Over Curves

Explore Manin's conjecture and its implications for counting rational points on smooth Fano varieties in this 58-minute lecture. Delve into the importance of excluding rational points from exceptional sets to accurately reflect the global geometry of the underlying variety. Examine applications of exceptional set studies to moduli spaces of sections of Fano fibrations, with a focus on how these sets explain pathological components in the moduli space. Learn about the specific case of del Pezzo fibrations, based on joint work with Brian Lehmann and Eric Riedl. Gain insights into the asymptotic formula for counting functions and its relationship to geometric invariants in this advanced mathematical exploration presented by Sho Tanimoto at the Hausdorff Center for Mathematics.