Baer cones in finite projective spaces
type: Item
instance of: scholarly article
title: Baer cones in finite projective spaces
zbMATH Open document ID: 0613.51006
DOI: 10.1007/BF01221941
author: Michael Huber
published in: Journal of Geometry
publication date: 1987-01-01T00:00:00Z
review text: Let \(V=PG(v,q)\). Suppose that V contains \(V^*=PG(v,\sqrt{q})\). Then \(V^*\) is said to be a Baer subspace of V. Suppose that PG(d,q), \(d\geq 3\) contains two skew subspaces V and R, where \(R=PG(r,q)\). Let C be the union of the subspaces generated by R and P, where P varies over V. Then C is called a Baer cone with radical r. A (t,s) blocking set in PG(d,q) is a set B of points such that \((1)\quad Each\) subspace of codimension t intersects B non-trivially. \((2)\quad Each\) s-dimensional subspace contains at least one point outside of B. The main result is that if B is a (t,s) blocking set with \(q\geq 5\), \(t\geq s-1,\) then \(| B| \geq q^ t+...+1+\sqrt{q}\quad (q^{t- 1}+...+q^{s-1})\) and equality holds if and only if B is a Baer cone of type \((s-2,^ 2(t-s+1)).\) This is a sequel to a previous paper of the author in Geom. Dedicata 18, 197-211 (1985; Zbl 0566.51009).
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 3992300
zbMATH Keywords: Baer cones in finite projective spaces
zbMATH Keywords: blocking set
reviewed by: Theodore G. Ostrom
MaRDI profile type: Publication
cites work: Q3331822
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description: scientific article; zbMATH DE number 3992300