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.
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页码：228 / 258
页数：31
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