Lines generate the Picard groups of certain Fermat surfaces

preprint2014arXivOpen access

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 $Φ_m$ is generated by the classes of lines contained in $Φ_m$ .

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Lines generate the Picard groups of certain Fermat surfaces

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