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June 2003 Quasi-subgeometry partitions of projective spaces
Norman Johnson
Bull. Belg. Math. Soc. Simon Stevin 10(2): 231-261 (June 2003). DOI: 10.36045/bbms/1054818026


The notion of a subgeometry partition of a finite projective space $% PG(2m-1,q^{2})$ by $PG(m-1,q^{2})$'s and $PG(2m-1,q)$'s or a partition of $% PG(2m,q^{2})$ by $PG(2m,q)$'s is generalized to quasi-subgeometry partitions of $PG(2m-1,q^{d})$ by $PG(dm/e-1,q^{e})$'s for a set of divisors $e$ of $d$ and, partitions of $PG(2m,q^{2d})$ by $PG(d(2m+1)/f-1,q^{f})$'s for a set of divisors $f$ of $d$. In all cases, there are associated vector space spreads that are unions of `fans'.

More generally, in the arbitrary dimensional case, a complete theory of quasi-subgeometry partitions of $PG(V-1,D)$ corresponding to generalized spreads admitting $D^{\ast }$ as a fixed-point-free collineation group is obtained. When $D$ is a quadratic extension of a base field, `subgeometry' partitions are obtain.


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Norman Johnson. "Quasi-subgeometry partitions of projective spaces." Bull. Belg. Math. Soc. Simon Stevin 10 (2) 231 - 261, June 2003.


Published: June 2003
First available in Project Euclid: 5 June 2003

zbMATH: 1045.51005
MathSciNet: MR2015201
Digital Object Identifier: 10.36045/bbms/1054818026

Primary: 51E23
Secondary: 51A40

Rights: Copyright © 2003 The Belgian Mathematical Society


Vol.10 • No. 2 • June 2003
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