Integral points of bounded height on partial equivariant compactifications of vector groups

TL;DR

This paper derives asymptotic formulas for counting integral points of bounded height on specific algebraic varieties called partial equivariant compactifications of vector groups, advancing understanding in Diophantine geometry.

Contribution

It provides the first asymptotic formulas for integral points on these compactifications, extending previous work on related algebraic varieties.

Findings

Asymptotic formulas for integral points established

Quantitative growth rates of points determined

New techniques for counting points on compactifications

Abstract

We establish asymptotic formulas for the number of integral points of bounded height on partial equivariant compactifications of vector groups.