Planes in cubic fourfolds

IF 1.2 1区数学 Q1 MATHEMATICS

Algebraic Geometry Pub Date : 2021-05-28 DOI:10.14231/ag-2023-007

A. Degtyarev, I. Itenberg, J. C. Ottem

引用次数: 1

Abstract

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.

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四层立体平面

我们证明了${\mathbb P}^5$中复光滑三次方四重中的最大平面数为$405$，仅由Fermat三次方实现；实光滑三次四重中实平面的最大数目是$357$，由所谓的Clebsch-Segre三次实现。总的来说，只有三个（直到投影等价）立方体的平面超过350$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebraic Geometry Mathematics-Geometry and Topology

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

52 weeks

期刊介绍： This journal is an open access journal owned by the Foundation Compositio Mathematica. The purpose of the journal is to publish first-class research papers in algebraic geometry and related fields. All contributions are required to meet high standards of quality and originality and are carefully screened by experts in the field.