Integral points of bounded height on quintic del Pezzo surfaces over number fields

TL;DR

This paper establishes an asymptotic count for integral points of bounded height on certain quintic del Pezzo surfaces over number fields, advancing understanding of their arithmetic geometry.

Contribution

It provides the first asymptotic formula for integral points of bounded height on split smooth quintic del Pezzo surfaces over number fields.

Findings

Asymptotic formula for integral points established

Results apply to surfaces with respect to a boundary line

Advances understanding of rational points on del Pezzo surfaces

Abstract

We prove an asymptotic formula for the number of integral points of bounded log-anticanonical height on split smooth quintic del Pezzo surfaces over number fields, with respect to one of the lines as the boundary divisor.