Lines generate the Picard groups of certain Fermat surfaces

Abstract

We answer a question of T.Shioda and show that, for any positive integer $m$ prime to 6, the Picard group of the Fermat surface ${\Phi }_m$ is generated by the classes of lines contained in ${\Phi }_m$.

revised and substantially extended (for non-topologists) version; title changed

References in corpus (2)

• On the Picard group of a Delsarte surface
• On the topology of projective subspaces in complex Fermat varieties

Cited by in corpus (2)

• Integral Hodge conjecture for Fermat varieties
• Mirror symmetry for K3 surfaces