On the rational points in conics of a cubic surfac

TL;DR

This paper establishes a uniform upper bound on the number of rational points of bounded height on conics lying on a cubic surface, using a generalized global determinant method via Arakelov geometry.

Contribution

It introduces a generalized version of Salberger's global determinant method employing Arakelov geometry to bound rational points on conics in cubic surfaces.

Findings

Provides a uniform upper bound for rational points on conics in cubic surfaces.

Extends the global determinant method with Arakelov geometry.

Enhances understanding of rational points distribution in algebraic geometry.

Abstract

In this paper, we give a uniform upper bound on the rational points of bounded height provided by conics in a cubic surface. For this target, we give a generalized version of the global determinant method of Salberger by Arakelov geometry.