Abstract
We prove that the only symplectic semifield spreads of \(\hbox {PG}(5,q^2)\), \(q\ge 2^{14}\) even, whose associated semifield has center containing \({\mathbb F}_q\), is the Desarguesian spread, by proving that the only \({\mathbb F}_q\)-linear set of rank 6 disjoint from the secant variety of the Veronese surface of \(\hbox {PG}(5,q^2)\) is a plane with three points of the Veronese surface of \(\hbox {PG}(5,q^6){\setminus } \hbox {PG}(5,q^2)\).
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Notes
\(\hbox {Fix}\, \sigma \) is the set of points fixed by \(\sigma \).
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The authors acknowledge the support of the project “Polinomi ortogonali, strutture algebriche e geometriche inerenti a grafi e campi finiti” of the SBAI Department of Sapienza University of Rome.
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Capparelli, S., Pepe, V. On symplectic semifield spreads of \(\hbox {PG}(5,q^2)\), q even. J Algebr Comb 46, 275–286 (2017). https://doi.org/10.1007/s10801-017-0742-x
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DOI: https://doi.org/10.1007/s10801-017-0742-x