We prove that the projective space PG(5,q) can be partitioned into two planes and q^3−1 caps all of which are quadric Veroneseans. This partition is obtained by taking the orbits of alifted Singer cycle of PG(2,q). The possibility of getting larger caps by gluing some of these orbits together is also addressed.
Mixed Partitions of PG(5,q) / R. D., Baker; Bonisoli, Arrigo; A., Cossidente; G. L., Ebert. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 208/209:(1999), pp. 23-29.
Mixed Partitions of PG(5,q)
BONISOLI, Arrigo;
1999
Abstract
We prove that the projective space PG(5,q) can be partitioned into two planes and q^3−1 caps all of which are quadric Veroneseans. This partition is obtained by taking the orbits of alifted Singer cycle of PG(2,q). The possibility of getting larger caps by gluing some of these orbits together is also addressed.
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