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Hermitian Varieties in a Finite Projective Space PG(N, q2)

Published online by Cambridge University Press:  20 November 2018

R. C. Bose  and
I. M. Chakravarti
R. C. Bose
Affiliation:
University of North Carolina
I. M. Chakravarti
Affiliation:
University of North Carolina
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The geometry of quadric varieties (hypersurfaces) in finite projective spaces of N dimensions has been studied by Primrose (12) and Ray-Chaudhuri (13). In this paper we study the geometry of another class of varieties, which we call Hermitian varieties and which have many properties analogous to quadrics. Hermitian varieties are defined only for finite projective spaces for which the ground (Galois field) GF(q2) has order q2, where q is the power of a prime. If h is any element of GF(q2), then = hq is defined to be conjugate to h.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1161 - 1182
Copyright
Copyright © Canadian Mathematical Society 1966

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