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Blockades and baer subspaces in finite projective spaces

✍ Scribed by Johannes Ueberberg

Publisher
Springer
Year
1991
Tongue
English
Weight
788 KB
Volume
39
Category
Article
ISSN
0046-5755

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✦ Synopsis

Let P = PG(2t + 1, q) denote the projective space of order q and of dimension 2t + 1 ~> 3. A set Β£f of lines of P is called a blockade if it fulfills the following two conditions. 1. Every (t + 1)-dimensional subspace of P contains at least one line of ~o. 2. Ifx is the intersecting point of two lines of_W, then every (t + 1)-dimensional subspace of P through x contains at least one line of E through x.

The most interesting examples of these blockades are the geometric spreads and the line sets of Baer subspaces of P. In our main result we shall classify the blockades under the additional property that there exists a t-dimensional subspace T of P such that each point of T is incident with at most one line of ~Β’. As a corollary we determine the blockades of minimal cardinality.

πŸ“œ SIMILAR VOLUMES

Partial parallelisms in finite projectiv
Partial parallelisms in finite projective spaces
✍ Albrecht Beutelspacher πŸ“‚ Article πŸ“… 1990 πŸ› Springer 🌐 English βš– 262 KB

We show the existence of a parallelism of ~ -U, where ~ is a finite projective space and U is a subspace of~' with dim.~ -dim U = 2 ~. As a consequence we prove a lower bound for the maximum number of disjoint spreads of ~'.