Some p-ranks related to Hermitian varieties

We determine the p-rank of the incidence matrix of hyperplanes of PG( n, p e ) and points of a nondegenerate Hermitian variety. As a corollary, we obtain new bounds for the size of caps and the existence of ovoids in finite unitary spaces. This paper is a companion to an earlier work in which Blokhu...

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Bibliographic Details
Published in:Journal of statistical planning and inference 1996-12, Vol.56 (2), p.229-241
Main Author: Moorhouse, G.Eric
Format: Article
Language:English
Subjects:
Hermitian variety
Ovoid
p-rank
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Summary:We determine the p-rank of the incidence matrix of hyperplanes of PG( n, p e ) and points of a nondegenerate Hermitian variety. As a corollary, we obtain new bounds for the size of caps and the existence of ovoids in finite unitary spaces. This paper is a companion to an earlier work in which Blokhuis and this author ( J. Algebraic Combin. 4 (1995), 295–316) derive the analogous p-ranks for quadrics.
ISSN:0378-3758
1873-1171
DOI:10.1016/S0378-3758(96)00020-1