Lines generate the Picard groups of certain Fermat surfaces

TL;DR

This paper proves that for Fermat surfaces with certain parameters, the Picard group is generated by lines on the surface, answering a specific open question in algebraic geometry.

Contribution

It establishes that for Fermat surfaces with parameters prime to 6, the Picard group is generated by lines, providing a complete description in these cases.

Findings

Picard group of Fermat surfaces with m prime to 6 is generated by lines

Answers a question posed by T. Shiota

Advances understanding of algebraic cycles on 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 $\Phi_m$.