Symplectic semifield spreads of PG(5, qt), q even

Valentina Pepe

Abstract


Let q > 2 ⋅ 34t be even. We prove that the only symplectic semifield spread of PG(5, qt), whose associate semifield has center containing Fq, is the Desarguesian spread. Equivalently, a commutative semifield of order q3t, with middle nucleus containing Fqt and center containing Fq, is a field. We do that by proving that the only possible Fq-linear set of rank 3t in PG(5, qt) disjoint from the secant variety of the Veronese surface is a plane of PG(5, qt).


Keywords


Semifields, spreads, symplectic polarity, linear sets, Veronese variety

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DOI: https://doi.org/10.26493/1855-3974.1763.6cb

ISSN: 1855-3974

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