Journal of the Institute of Mathematics of Jussieu



UNIRATIONALITY OF CUBIC HYPERSURFACES


János Kollár a1
a1 Department of Mathematics, Princeton University, Princeton, NJ 08544-1000, USA (kollar@math.princeton.edu)

Abstract

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.