3:30-4:30 pm, Seminar Hall
Manin's conjecture and the Fujita invariant of finite covers
Let $X$ be a Fano variety defined over a number field. Manin's conjecture predicts an asymptotic formula for the number of rational points on $X$ with bounded height. According to the conjecture, the growth of rational points is governed by certain geometric invariants, namely the Fujita invariant (or the $a$-constant). In this talk we will discuss some recent progress in this area and use birational geometric methods to prove statements predicted by Manin's conjecture. In particular, we will study the behavior of the Fujita invariant under pull-back to generically finite covers and prove a statement about geometric consistency of Manin's conjecture.