On quasi-Hermitian varieties in \(\operatorname{PG}(3, q^2)\)
type: Item
instance of: scholarly article
title: On quasi-Hermitian varieties in \(\operatorname{PG}(3, q^2)\)
zbMATH Open document ID: 1331.51009
author: V. Napolitano
published in: Discrete Mathematics
publication date: 2015-12-08T00:00:00Z
review text: The author gives two combinatorial characterizations of the Hermitian surface of the finite 3-dimensional projective space in terms of quasi-Hermitian varieties. Specifically, he proves the following results. If \(s\) and \(t\) are integers with \(0 \leq s <t \leq q^2-1\) then a quasi-Hermitian variety of \(\mathrm{PG}(3,q^2)\) of line class \([s+1,t+1,q^2+1]_1\) is a Hermitian variety of \(\mathrm{PG}(3,q^2)\). In \(\mathrm{PG}(3,q^2)\) a quasi-Hermitian variety of line class \([1,q+1,\dots, q^2+1]_1\) is a Hermitian variety of \(\mathrm{PG}(3,q^2)\).
reviewed by: Steven T. Dougherty
Mathematics Subject Classification ID: 51E30
zbMATH DE Number: 6517654
zbMATH Keywords: projective space
zbMATH Keywords: intersection number
zbMATH Keywords: Hermitian variety
MaRDI profile type: Publication
full work available at URL: j.disc.2015.09.013
OpenAlex ID: W2204331052
cites work: Q5499942
cites work: On Quasi-Hermitian Varieties
cites work: On sets of type \((m,n)_{r - 1}\) in PG\((r,q)\)
cites work: The Geometry of Two-Weight Codes
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DOI: 10.1016/J.DISC.2015.09.013
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description: scientific article; zbMATH DE number 6517654