Geometric invariants and geometric consistency of Manin's conjecture.

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 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.

algebraic geometrynumber theory

Audience: researchers in the topic

CMI seminar series

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