Manin's conjecture on toric varieties with different heights

TL;DR

This paper verifies Manin's conjecture for certain rational projective toric varieties using a broad class of height functions beyond the standard metric, advancing understanding of rational points distribution.

Contribution

It extends Manin's conjecture verification to toric varieties with diverse height functions, broadening the scope of previous results.

Findings

Confirmed Manin's conjecture for specific toric varieties

Established results for various height functions

Enhanced understanding of rational points distribution on toric varieties

Abstract

In this paper I verify Manin's conjecture for a class of rational projective toric varieties with a large class of heights other than the usual one that comes from the standard metric on projective space.