Planes in cubic fourfolds
Algebraic Geometry
2024-08-20 v2
Abstract
We show that the maximal number of planes in a complex smooth cubic fourfold in is , realized by the Fermat cubic only; the maximal number of real planes in a real smooth cubic fourfold is , realized by the so-called Clebsch--Segre cubic. Altogether, there are but three (up to projective equivalence) cubics with more than planes.
Keywords
Cite
@article{arxiv.2105.13951,
title = {Planes in cubic fourfolds},
author = {Alex Degtyarev and Ilia Itenberg and John Christian Ottem},
journal= {arXiv preprint arXiv:2105.13951},
year = {2024}
}
Comments
Revise version accepted for publication. Newer references and a bound for nodal cubics added