Geometric invariants and geometric consistency of Manin's conjecture.

by Dr. Akash Kumar Sengupta (Columbia University)

Friday, November 6, 2020 from 05:30 to 06:30 (Asia/Kolkata)
at Over Zoom

Description

Abstract: Let X be a Fano variety with an associated height function
defined over a number field. Manin's conjecture predicts that, after
removing a thin set, the asymptotic growth of the number of rational
points of bounded height on X is controlled by certain geometric
invariants (e.g. the Fujita invariant of X). I will talk about how to use
birational geometric methods to study the behaviour of these invariants
and propose a geometric description of the thin set in Manin's conjecture.
Part of this is joint work with Brian Lehmann and Sho Tanimoto.