Geodesic
Symplectic semifield spreads of PG(5, q^t), q even
Ars Mathematica Contemporanea, Tome 17 (2019) no. 2, pp. 515-524.

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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).
DOI : 10.26493/1855-3974.1763.6cb
Keywords: Semifields, spreads, symplectic polarity, linear sets, Veronese variety 
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Valentina Pepe. Symplectic semifield spreads of PG(5, q^t), q even. Ars Mathematica Contemporanea, Tome 17 (2019) no. 2, pp. 515-524. doi : 10.26493/1855-3974.1763.6cb. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1763.6cb/

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