Number Theory Seminar

Speaker: Marta Pieropan (Hannover)

Title: On the distribution of rational points on Fano varieties over number fields.

Abstract: After introducing the natural questions around rational points on varieties over number fields, we focus on Manin's conjecture about the distribution of rational points on Fano varieties. This conjecture predicts an asymptotic formula for the number of points of bounded anticanonical height that is intimately related to the geometry of the variety. We see how Cox rings and universal torsors can be employed to produce parameterizations that are used to verify the conjecture in some specific cases.