UNIRATIONALITY OF CUBIC HYPERSURFACES
Segre proved that a smooth cubic surface over $Q$ is unirational if and only if it has a rational point. We prove that the result also holds for cubic hypersurfaces over any field, including finite fields.
AMS 2000 Mathematics subject classification: Primary 14G05; 14G15. Secondary 11G25; 11D25(Received February 15 2001)
(Accepted June 5 2001)
Key Words: cubic hypersurface; unirational; rational points.