On the Neron-Severi group of surfaces with many lines

Abstract

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

To appear in Proc. AMS