Planes in cubic fourfolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866909289503784960 |
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| author | Degtyarev, Alex Itenberg, Ilia Ottem, John Christian |
| author_facet | Degtyarev, Alex Itenberg, Ilia Ottem, John Christian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_13951 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Planes in cubic fourfolds Degtyarev, Alex Itenberg, Ilia Ottem, John Christian Algebraic Geometry 14J35, 14N20, 14N25, 14P25 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. |
| title | Planes in cubic fourfolds |
| topic | Algebraic Geometry 14J35, 14N20, 14N25, 14P25 |
| url | https://arxiv.org/abs/2105.13951 |