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Some p-ranks related to Hermitian varieties

โœ Scribed by G.Eric Moorhouse

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
625 KB
Volume
56
Category
Article
ISSN
0378-3758

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โœฆ Synopsis

We determine the p-rank of the incidence matrix of hyperplanes of PG(n, pC) 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.

๐Ÿ“œ SIMILAR VOLUMES

Some p-ranks related to a conic in PG(2,
Some p-ranks related to a conic in PG(2, q)
โœ Junhua Wu ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 144 KB ๐Ÿ‘ 1 views

## Abstract Let A be the incidence matrix of lines and points of the classical projective plane __PG__(2, __q__) with __q__ odd. With respect to a conic in __PG__(2, __q__), the matrix A is partitioned into 9 submatrices. The rank of each of these submatrices over __F__~__q__~, the defining field o