Geometric consistency of Manin's conjecture

By Brian Lehmann, Akash Kumar Sengupta, Sho Tanimoto. Compositio Mathematica, 2018

47 citations recorded by the source corpus.

We conjecture that the exceptional set in Manin's conjecture has an explicit geometric description. Our proposal includes the rational point contributions from any generically finite map with larger geometric invariants. We prove that this set is contained in a thin subset of rational points, verifying that there is no counterexample to Manin's conjecture which arises from an incompatibility of geometric invariants.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/41df2bb0e8bda056e901b01b66b96e13267cf09e

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In Geometry and Topology

1. David Zureick-Brown
2. Matthew Satriano
3. Jordan S. Ellenberg
4. Kiran S. Kedlaya
5. Michael A. Bennett
6. 'Alvaro Lozano-Robledo

Citations in the corpus

• Heights on stacks and a generalized Batyrev–Manin–Malle conjecture (2021, background): “14 geometrically consistent in the sense of Lehmann, Sengupta and Tanimoto [47]? ◦ How should one estimate the asymptotic growth of points on X which are integral with respect to a divisor D? ◦ As mentioned earlier in the paper, one might, rather than defining height in terms of the degree of π∗x ∗V”