Semi-integral points of bounded height on vector group compactifications

TL;DR

This paper proves the Manin conjecture for Darmon points on vector group compactifications and calculates leading constants in specific cases, advancing understanding of rational points on algebraic varieties.

Contribution

It establishes the Manin conjecture for a new class of points and computes explicit constants, extending previous work on rational points.

Findings

Proof of Manin conjecture for Darmon points

Calculation of leading constants in examples

Extension of techniques to vector group compactifications

Abstract

In this article, we prove the Manin conjecture for Darmon points on vector group compactifications using ideas similar to those in [PSTVA21]. We also calculate the leading constants in some examples.