Ricerche di Matematica

, Volume 60, Issue 1, pp 125–142 | Cite as

Symplectic semifield spreads of PG(5, q) and the veronese surface

  • G. Lunardon
  • G. Marino
  • O. Polverino
  • R. Trombetti
Article
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Abstract

In this paper we show that starting from a symplectic semifield spread \({\mathcal{S}}\) of PG(5, q), q odd, another symplectic semifield spread of PG(5, q) can be obtained, called the symplectic dual of \({\mathcal{S}}\), and we prove that the symplectic dual of a Desarguesian spread of PG(5, q) is the symplectic semifield spread arising from a generalized twisted field. Also, we construct a new symplectic semifield spread of PG(5, q) (q = s 2, s odd), we describe the associated commutative semifield and deal with the isotopy issue for this example. Finally, we determine the nuclei of the commutative pre-semifields constructed by Zha et al. (Finite Fields Appl 15(2):125–133, 2009).

Keywords

Symplectic semifield Spread set Isotopy 

Mathematics Subject Classification (2000)

12K10 51A40 51E99 
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Copyright information

© Università degli Studi di Napoli "Federico II" 2010

Authors and Affiliations

  • G. Lunardon
    • 1
  • G. Marino
    • 2
  • O. Polverino
    • 2
  • R. Trombetti
    • 1
  1. 1.Dipartimento di Matematica e ApplicazioniUniversitá degli Studi di Napoli “Federico II”NaplesItaly
  2. 2.Dipartimento di MatematicaSeconda Università degli Studi di NapoliCasertaItaly

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