Baer cones in finite projective spaces
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).
scientific article; zbMATH DE number 3992300