Geometric consistency of Manin's conjecture. Issue 6 (22nd June 2022)

• Record Type: Journal Article
• Authors: Lehmann, Brian; Sengupta, Akash Kumar; Tanimoto, Sho
• Is Part Of: Compositio mathematica. Volume 158:Issue 6(2022)
• Page Start: 1375
• Page End: 1427
• Publication Date: 2022-06-22
• Subjects: Manin's conjecture -- exceptional set -- minimal model program; 14G05 -- 14E30; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X22007588
• Languages: English
• ISSNs: 0010-437X

Abstract

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.