Manin's conjecture for toric varieties

TL;DR

This paper proves Manin's conjecture on the asymptotic count of rational points of bounded height on smooth projective toric varieties over number fields.

Contribution

It establishes the conjectured asymptotic formula for the number of rational points on toric varieties, confirming Manin's conjecture in this setting.

Findings

Confirmed Manin's conjecture for all smooth projective toric varieties over number fields.

Derived explicit asymptotic formulas for counting rational points.

Extended previous results to a broader class of varieties.

Abstract

We prove an asymptotic formula conjectured by Manin for the number of $K$-rational points of bounded height with respect to the anticanonical line bundle for arbitrary smooth projective toric varieties over a number field $K$.