Geometric consistency of Manin's conjecture
Brian Lehmann, Akash Kumar Sengupta, Sho Tanimoto
Abstract
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.
Topics & Concepts
MathematicsCounterexampleConjecturePoint (geometry)Pure mathematicsConsistency (knowledge bases)Set (abstract data type)CombinatoricsDiscrete mathematicsGeometryComputer scienceProgramming languageAlgebraic Geometry and Number TheoryGeometry and complex manifoldsGeometric and Algebraic Topology