Planes in cubic fourfolds

被引：0

作者：

Degtyarev, Alex ^{[1
]}

Itenberg, Ilia ^{[2
,3
]}

Ottem, John Christian ^{[4
]}

机构：

[1] Bilkent Univ, Dept Math, TR-06800 Ankara, Turkiye

[2] Sorbonne Univ, F-75005 Paris, France

[3] Univ Paris Cite, CNRS, IMJ, PRG, F-75005 Paris, France

[4] Univ Oslo, Dept Math, Box 1053, N-0316 Oslo, Norway

来源：

ALGEBRAIC GEOMETRY | 2023年 / 10卷 / 02期

关键词：

cubic fourfold; integral lattice; Niemeier lattice; discriminant form; 2-planes;

D O I：

10.14231/AG-2023-007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：228 / 258

页数：31

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