On sets of planes in projective spaces intersecting mutually in one point

被引：10

作者：

Beutelspacher, A ^{[1
]}

Eisfeld, J ^{[1
]}

Müller, J ^{[1
]}

机构：

[1] Math Inst, D-35392 Giessen, Germany

来源：

GEOMETRIAE DEDICATA | 1999年 / 78卷 / 02期

关键词：

projective space; PG; Klein quadric; Fano plane;

D O I：

10.1023/A:1005294416997

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let P be a projective space. In this paper we consider sets E of planes of P such that any two planes of E intersect in exactly one point. Our investigation will lead to a classification of these sets in most cases. There are the following two main results: If E is a set of planes of a projective space intersecting mutually in one point, then the set of intersection points spans a subspace of dimension less than or equal to 6. There are up to isomorphism only three sets E where this dimension is 6. These sets are related to the Fano plane. If E is a set of planes of PG(d,q) intersecting mutually in one point, and if q greater than or equal to 3, \ E \greater than or equal to 3(q(2)+q+1), then E is either contained in a Klein quadric in PG(5,q), or E is a dual partial spread in PG(4,q), or all elements of E pass through a common point.

引用

页码：143 / 159

页数：17