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arXiv · 2105.13951

Planes in cubic fourfolds

Alex Degtyarev·Ilia Itenberg·John Christian Ottem
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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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Alex Degtyarev, Ilia Itenberg, John Christian Ottem. 2022-08-30. Planes in cubic fourfolds. https://doi.org/10.14231/ag-2023-007

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