On the Néron-Severi group of surfaces with many lines

Boissière, Samuel; Sarti, Alessandra

doi:10.1090/S0002-9939-08-09475-6

On the Néron-Severi group of surfaces with many lines
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by Samuel Boissière and Alessandra Sarti PDF

Proc. Amer. Math. Soc. 136 (2008), 3861-3867 Request permission

Abstract:

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

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