Unirationality of cubic hypersurfaces

J\'anos Koll\'ar (Princeton Univ.)

Unirationality of cubic hypersurfaces

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arxiv math/0005146 v1 pith:RIO6PHBK submitted 2000-05-15 math.AG

János Kollár (Princeton Univ.) This is my paper · ORCID

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keywords cubichypersurfacesfieldfieldsfiniteholdsincludingpoint

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Segre proved that a smooth cubic surface over Q is unirational iff it has a rational point. We prove that the result also holds for cubic hypersurfaces over any field, including finite fields.

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Anomaly cancellation for two $U(1)$ factors
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Abelian anomaly cancellation for rank-K U(1) summands equates to finding (K-1)-planes on a cubic hypersurface over Q; for K=2 and six fermions this is the Fano surface of the Segre cubic, whose rational components ful...

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