Abstract
We show that smooth cubic hypersurfaces of dimension n defined over a finite field \(\mathbf{F}_q\) contain a line defined over \(\mathbf{F}_q\) in each of the following cases: \(n=3\) and \(q\ge 11\); \(n=4\), and \(q=2\) or \(q\ge 5\); \(n\ge 5\).
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