Integral points on conic log K3 surfaces

TL;DR

This paper establishes explicit conditions for the existence of integral points on certain fibered schemes, including smooth log K3 surfaces, using an adaptation of Swinnerton-Dyer's method, marking a novel contribution in the field.

Contribution

It provides the first known set of explicit conditions for integral points on a family of log K3 surfaces, expanding the understanding of their arithmetic properties.

Findings

Explicit conditions for integral points on fibered schemes

Application to smooth log K3 surfaces

First such conditions established for this family

Abstract

Adapting a powerful method of Swinnerton-Dyer, we give explicit sufficient conditions for the existence of integral points on certain schemes which are fibered into affine conics. This includes, in particular, cases where the scheme is geometrically a smooth log K3 surface. To the knowledge of the author, this is the first family of log K3 surfaces for which such conditions are established.