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This is a Quantitative Study study.

October 16, 2025Open Access

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

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An asymptotic formula for integral points was established, showing the distribution of points with bounded height.
The study focuses on quintic del Pezzo surfaces over number fields, particularly alongside a designated boundary divisor.
The findings may have implications for understanding the structure of rational points on these surfaces.
The analysis centers on log-anticanonical height, contributing to the broader discourse on heights in arithmetic geometry.

Implication

The research demonstrates an asymptotic formula for integral points on quintic del Pezzo surfaces, indicating properties of bounded height.

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.

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Cite This Study

Bernert et al. (2025) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fd2bb https://doi.org/10.48550/arxiv.2505.10077

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Implication

The research demonstrates an asymptotic formula for integral points on quintic del Pezzo surfaces, indicating properties of bounded height.

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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