On the Neron-Severi group of surfaces with many lines

TL;DR

This paper classifies certain K3 surfaces with many lines and proves that for generic forms of prime degree, their Neron-Severi groups are generated by lines, revealing structural properties of these algebraic surfaces.

Contribution

It provides a classification of K3 surfaces with Neron-Severi groups generated by lines and extends results to generic prime degree forms.

Findings

Classified K3 surfaces with Neron-Severi groups generated by lines.

Proved that generic prime degree forms produce surfaces with Neron-Severi groups generated by lines.

Abstract

For a binary quartic form $\phi$ without multiple factors, we classify the quartic K3 surfaces $\phi(x,y)=\phi(z,t)$ whose Neron-Severi group is (rationally) generated by lines. For generic binary forms $\phi$, $\psi$ of prime degree without multiple factors, we prove that the Neron-Severi group of the surface $\phi(x,y)=\psi(z,t)$ is rationally generated by lines.