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Pré-Publication, Document De Travail Année : 2022

Planes in cubic fourfolds

Résumé

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.

Dates et versions

hal-04009268 , version 1 (01-03-2023)

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Alex Degtyarev, Ilia Itenberg, John Christian Ottem. Planes in cubic fourfolds. 2022. ⟨hal-04009268⟩
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