On symplectic semifield spreads of \(\mathrm{PG}(5,q^{2})\), \(q\) odd
type: Item
instance of: scholarly article
title: On symplectic semifield spreads of \(\mathrm{PG}(5,q^{2})\), \(q\) odd
zbMATH Open document ID: 1478.51001
author: Xianqiang Yang
published in: Forum Mathematicum
publication date: 2018-04-13T00:00:00Z
review text: This excellent paper yields a classification of semifield symplectic spreads of \(W(5,q^2)\) for \(q\) a large enough odd prime power (n.b., \(q\geqslant 121\)), and having a centre of the associated semifield containing \(\mathbb{F}_q\). The main idea is to exploit the connection between semifield symplectic spreads and certain sets of symmetric matrices known as \textit{spread sets}. These spread sets are in turn associated to linear sets, which are in turn contained in a subspace of a particular quadric Veronesean. There are precisely three such semifield symplectic spreads up to projective equivalence.
reviewed by: John Bamberg
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51A50
Mathematics Subject Classification ID: 12K10
Mathematics Subject Classification ID: 14M12
zbMATH DE Number: 6859568
zbMATH Keywords: commutative semifield
zbMATH Keywords: symplectic semifield spread
zbMATH Keywords: Veronese variety
MaRDI profile type: Publication
full work available at URL: forum-2016-0133
OpenAlex ID: W2746464959
cites work: Generalized twisted fields
cites work: Q4323109
cites work: New semifields, PN and APN functions
cites work: Commutative semifields from projection mappings
cites work: New Perfect Nonlinear Multinomials over F $_{p^{2k}}$ for Any Odd Prime p
cites work: Improved explicit estimates on the number of solutions of equations over a finite field
cites work: On symplectic semifield spreads of \(\mathrm{PG}(5,q^2)\), \(q\) even
cites work: Q5545191
cites work: Q4002797
cites work: Q4003762
cites work: Q3426902
cites work: Commutative semifields and symplectic spreads.
cites work: Finite semifields and projective planes
cites work: Finite semifields with a large nucleus and higher secant varieties to Segre varieties
cites work: Q3464678
cites work: Q3216750
cites work: Translation ovoids
cites work: Symplectic semifield spreads of \(\mathrm{PG}(5,q)\) and the Veronese surface
cites work: Translation ovoids of orthogonal polar spaces
cites work: Q3891315
cites work: On isotopisms and strong isotopisms of commutative presemifields
cites work: On the nuclei of a finite semifield
cites work: Q4832256
cites work: On a Kaplansky conjecture concerning three-dimensional division algebras over a finite field
cites work: Linear sets in finite projective spaces
cites work: Perfect nonlinear binomials and their semifields
cites work: A new family of semifields with 2 parameters
DOI: 10.1515/FORUM-2016-0133
description: scientific article; zbMATH DE number 6859568