Planes in cubic fourfolds

Degtyarev, Alex; Itenberg, Ilia; Ottem, John Christian

doi:10.14231/AG-2023-007

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Planes in cubic fourfolds

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Degtyarev, Alex
Max Planck Institute for Mathematics, Max Planck Society;

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Itenberg, Ilia
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.14231/AG-2023-007
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https://doi.org/10.48550/arXiv.2105.13951
(Preprint)

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Degtyarev-Itenberg-Otten_Planes in cubic fourfolds_2023.pdf
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Citation

Degtyarev, A., Itenberg, I., & Ottem, J. C. (2023). Planes in cubic fourfolds. Algebraic Geometry, 10(2), 228-258. doi:10.14231/AG-2023-007.

Cite as: https://hdl.handle.net/21.11116/0000-000C-CEE8-7

Abstract

We show that the maximal number of planes in a complex smooth cubic fourfold in P5
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