Work

Manin's conjecture for integral points on toric varieties

Year: 2026

Type: article

Abstract: We formulate a conjecture on the number of integral points of bounded height on log Fano varieties in analogy with Manin's conjecture on the number of rational points of bounded height on Fano varieties. We also give a prediction for the leading constant that is similar to Peyre's interpretation of the leading constant in Manin's conjecture. We give evidence for our conjecture by proving it for toric varieties. The proof is based on harmonic analysis on universal torsors.

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms.70203

Author: Tim Santens

Institution: University of Cambridge

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,700

Funders: Fonds Wetenschappelijk Onderzoek, Vlaamse regering