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Planes in cubic fourfolds

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arxiv 2105.13951 v2 pith:73SLQWCN submitted 2021-05-28 math.AG

Alex Degtyarev , Ilia Itenberg , John Christian Ottem This is my paper
classification math.AG
keywords cubicplanesfourfoldmaximalnumberrealrealizedsmooth
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abstract

We show that the maximal number of planes in a complex smooth cubic fourfold in ${\mathbb P}^5$ is $405$, realized by the Fermat cubic only; the maximal number of real planes in a real smooth cubic fourfold is $357$, realized by the so-called Clebsch--Segre cubic. Altogether, there are but three (up to projective equivalence) cubics with more than $350$ planes.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Anomaly cancellation for two $U(1)$ factors

    hep-th 2026-07 accept novelty 7.0 of 10

    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...

  2. Rational cubic fourfolds with a symplectic group of automorphisms

    math.AG 2025-09 conditional novelty 5.0 of 10

    Cubic fourfolds admitting a cyclic group of symplectic automorphisms of order not a power of 2 are rational and lie in the Hassett divisors C_14 or C_42.

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