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UNIRATIONALITY OF CUBIC HYPERSURFACES

Published online by Cambridge University Press:  25 June 2002

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

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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

Keywords

cubic hypersurfaceunirationalrational points
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 1 , Issue 3 , July 2002 , pp. 467 - 476
Copyright
2002 Cambridge University Press