Hermitian Configurations in Odd-Dimensional Projective Geometries
1981 ◽
Vol 33
(2)
◽
pp. 500-512
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A t-cap in a geometry is a set of t points no three of which are collinear. A (t, k)-cap is a set of t points, no k + 1 of which are collinear.It has been shown in [3] that any Desarguesian PG(2n, q2) is a disjoint union of (q2n+l – l)/(q – 1) (q2n+l – l)/(q + l)-caps. These caps were obtained as intersections of 2n Hermitian Varieties of a certain kind; the intersection of 2n + 1 such varieties was empty. Furthermore, the caps in question constituted the ‘large points” of a PG(2n, q), with the incidence relation defined in a natural way.It seemed at the time that nothing similar could be said about odd-dimensional projective geometries, if only because |PG(2n – 1, q)| ∤ |PG(2n – l, q2)|.
1980 ◽
Vol 32
(6)
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pp. 1299-1305
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Keyword(s):
2006 ◽
Vol 15
(06)
◽
pp. 761-772
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1985 ◽
Vol 37
(6)
◽
pp. 1163-1175
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2019 ◽
Vol 19
(1)
◽
pp. 80-88
Keyword(s):
2018 ◽
Keyword(s):